LMFDB - Embedded newform 418.2.f.f.115.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(115,418)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([4, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("418.115");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.f (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 24 x^{14} - 62 x^{13} + 148 x^{12} - 232 x^{11} + 432 x^{10} - 356 x^{9} + 424 x^{8} + \cdots + 16 $ x^16 - 6x^15 + 24x^14 - 62x^13 + 148x^12 - 232x^11 + 432x^10 - 356x^9 + 424x^8 - 320x^7 + 712x^6 - 936x^5 + 968x^4 - 336x^3 + 208x^2 - 80*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			115.2
Root			$-0.628609 - 1.93466i$ of defining polynomial
Character	$\chi$	$=$	418.115
Dual form			418.2.f.f.229.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.951057i) q^{2} +(-0.738622 - 0.536641i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.549198 + 1.69026i) q^{5} +(0.282129 - 0.868303i) q^{6} +(4.08354 - 2.96686i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.669471 - 2.06042i) q^{9} +O(q^{10})$	\(q+(0.309017 + 0.951057i) q^{2} +(-0.738622 - 0.536641i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.549198 + 1.69026i) q^{5} +(0.282129 - 0.868303i) q^{6} +(4.08354 - 2.96686i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.669471 - 2.06042i) q^{9} -1.77724 q^{10} +(2.07982 - 2.58348i) q^{11} +0.912987 q^{12} +(1.67602 + 5.15825i) q^{13} +(4.08354 + 2.96686i) q^{14} +(1.31271 - 0.953740i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-0.563182 + 1.73330i) q^{17} +(1.75270 - 1.27341i) q^{18} +(0.809017 + 0.587785i) q^{19} +(-0.549198 - 1.69026i) q^{20} -4.60833 q^{21} +(3.09973 + 1.17969i) q^{22} +5.61764 q^{23} +(0.282129 + 0.868303i) q^{24} +(1.48974 + 1.08236i) q^{25} +(-4.38787 + 3.18797i) q^{26} +(-1.45760 + 4.48605i) q^{27} +(-1.55977 + 4.80049i) q^{28} +(-1.81205 + 1.31653i) q^{29} +(1.31271 + 0.953740i) q^{30} +(0.119445 + 0.367612i) q^{31} +1.00000 q^{32} +(-2.92260 + 0.792100i) q^{33} -1.82249 q^{34} +(2.77209 + 8.53162i) q^{35} +(1.75270 + 1.27341i) q^{36} +(8.16517 - 5.93234i) q^{37} +(-0.309017 + 0.951057i) q^{38} +(1.53018 - 4.70942i) q^{39} +(1.43782 - 1.04464i) q^{40} +(-7.51036 - 5.45660i) q^{41} +(-1.42405 - 4.38278i) q^{42} +5.45957 q^{43} +(-0.164078 + 3.31256i) q^{44} +3.85031 q^{45} +(1.73595 + 5.34269i) q^{46} +(-8.74809 - 6.35586i) q^{47} +(-0.738622 + 0.536641i) q^{48} +(5.70988 - 17.5732i) q^{49} +(-0.569028 + 1.75129i) q^{50} +(1.34613 - 0.978024i) q^{51} +(-4.38787 - 3.18797i) q^{52} +(2.11890 + 6.52132i) q^{53} -4.71691 q^{54} +(3.22451 + 4.93427i) q^{55} -5.04753 q^{56} +(-0.282129 - 0.868303i) q^{57} +(-1.81205 - 1.31653i) q^{58} +(-2.99725 + 2.17763i) q^{59} +(-0.501411 + 1.54318i) q^{60} +(0.893988 - 2.75141i) q^{61} +(-0.312710 + 0.227197i) q^{62} +(-8.84680 - 6.42757i) q^{63} +(0.309017 + 0.951057i) q^{64} -9.63923 q^{65} +(-1.65646 - 2.53478i) q^{66} -11.5655 q^{67} +(-0.563182 - 1.73330i) q^{68} +(-4.14931 - 3.01465i) q^{69} +(-7.25743 + 5.27283i) q^{70} +(-0.269698 + 0.830045i) q^{71} +(-0.669471 + 2.06042i) q^{72} +(-7.91393 + 5.74981i) q^{73} +(8.16517 + 5.93234i) q^{74} +(-0.519516 - 1.59891i) q^{75} -1.00000 q^{76} +(0.828188 - 16.7203i) q^{77} +4.95177 q^{78} +(2.87944 + 8.86201i) q^{79} +(1.43782 + 1.04464i) q^{80} +(-1.77408 + 1.28895i) q^{81} +(2.86870 - 8.82896i) q^{82} +(-1.32476 + 4.07720i) q^{83} +(3.72822 - 2.70871i) q^{84} +(-2.62042 - 1.90384i) q^{85} +(1.68710 + 5.19236i) q^{86} +2.04493 q^{87} +(-3.20114 + 0.867591i) q^{88} -5.60537 q^{89} +(1.18981 + 3.66186i) q^{90} +(22.1479 + 16.0914i) q^{91} +(-4.54476 + 3.30196i) q^{92} +(0.109051 - 0.335626i) q^{93} +(3.34147 - 10.2840i) q^{94} +(-1.43782 + 1.04464i) q^{95} +(-0.738622 - 0.536641i) q^{96} +(-0.897782 - 2.76309i) q^{97} +18.4776 q^{98} +(-6.71543 - 2.55574i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} - 4 q^{4} + 4 q^{5} + 6 q^{7} - 4 q^{8} - 20 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 - 4 * q^4 + 4 * q^5 + 6 * q^7 - 4 * q^8 - 20 * q^9	$ 16 q - 4 q^{2} - 4 q^{4} + 4 q^{5} + 6 q^{7} - 4 q^{8} - 20 q^{9} + 4 q^{10} + 2 q^{11} - 14 q^{13} + 6 q^{14} - 10 q^{15} - 4 q^{16} + 8 q^{17} + 4 q^{19} + 4 q^{20} + 28 q^{21} + 2 q^{22} + 24 q^{23} - 4 q^{26} - 18 q^{27} - 14 q^{28} - 22 q^{29} - 10 q^{30} - 24 q^{31} + 16 q^{32} + 2 q^{33} + 8 q^{34} - 20 q^{35} + 6 q^{37} + 4 q^{38} + 72 q^{39} - 6 q^{40} - 14 q^{41} - 22 q^{42} + 56 q^{43} + 12 q^{44} - 56 q^{45} + 4 q^{46} - 38 q^{47} - 36 q^{49} + 56 q^{51} - 4 q^{52} + 22 q^{53} - 48 q^{54} - 6 q^{55} + 16 q^{56} - 22 q^{58} - 28 q^{59} + 12 q^{61} + 26 q^{62} - 20 q^{63} - 4 q^{64} - 32 q^{65} + 12 q^{66} - 44 q^{67} + 8 q^{68} + 64 q^{69} - 20 q^{70} + 16 q^{71} - 20 q^{72} + 12 q^{73} + 6 q^{74} + 32 q^{75} - 16 q^{76} - 12 q^{77} - 8 q^{78} + 48 q^{79} - 6 q^{80} - 64 q^{81} + 6 q^{82} + 14 q^{83} + 8 q^{84} + 6 q^{85} - 14 q^{86} + 84 q^{87} - 8 q^{88} - 56 q^{89} + 34 q^{90} + 26 q^{91} - 16 q^{92} - 46 q^{93} + 32 q^{94} + 6 q^{95} - 24 q^{97} + 64 q^{98} - 56 q^{99}+O(q^{100}) $ 16 * q - 4 * q^2 - 4 * q^4 + 4 * q^5 + 6 * q^7 - 4 * q^8 - 20 * q^9 + 4 * q^10 + 2 * q^11 - 14 * q^13 + 6 * q^14 - 10 * q^15 - 4 * q^16 + 8 * q^17 + 4 * q^19 + 4 * q^20 + 28 * q^21 + 2 * q^22 + 24 * q^23 - 4 * q^26 - 18 * q^27 - 14 * q^28 - 22 * q^29 - 10 * q^30 - 24 * q^31 + 16 * q^32 + 2 * q^33 + 8 * q^34 - 20 * q^35 + 6 * q^37 + 4 * q^38 + 72 * q^39 - 6 * q^40 - 14 * q^41 - 22 * q^42 + 56 * q^43 + 12 * q^44 - 56 * q^45 + 4 * q^46 - 38 * q^47 - 36 * q^49 + 56 * q^51 - 4 * q^52 + 22 * q^53 - 48 * q^54 - 6 * q^55 + 16 * q^56 - 22 * q^58 - 28 * q^59 + 12 * q^61 + 26 * q^62 - 20 * q^63 - 4 * q^64 - 32 * q^65 + 12 * q^66 - 44 * q^67 + 8 * q^68 + 64 * q^69 - 20 * q^70 + 16 * q^71 - 20 * q^72 + 12 * q^73 + 6 * q^74 + 32 * q^75 - 16 * q^76 - 12 * q^77 - 8 * q^78 + 48 * q^79 - 6 * q^80 - 64 * q^81 + 6 * q^82 + 14 * q^83 + 8 * q^84 + 6 * q^85 - 14 * q^86 + 84 * q^87 - 8 * q^88 - 56 * q^89 + 34 * q^90 + 26 * q^91 - 16 * q^92 - 46 * q^93 + 32 * q^94 + 6 * q^95 - 24 * q^97 + 64 * q^98 - 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$3$	−0.738622	−	0.536641i	−0.426444	−	0.309830i	0.353782	−	0.935328i	$-0.384896\pi$
$3$	−0.738622	−	0.536641i	−0.426444	−	0.309830i	−0.780225	+	0.625499i	$0.784896\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	−0.549198	+	1.69026i	−0.245609	+	0.755906i	0.749927	+	0.661520i	$0.230089\pi$
$5$	−0.549198	+	1.69026i	−0.245609	+	0.755906i	−0.995536	+	0.0943852i	$0.969911\pi$
$6$	0.282129	−	0.868303i	0.115179	−	0.354483i
$7$	4.08354	−	2.96686i	1.54343	−	1.12137i	0.595295	−	0.803507i	$-0.297035\pi$
$7$	4.08354	−	2.96686i	1.54343	−	1.12137i	0.948137	−	0.317862i	$-0.102965\pi$
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	−0.669471	−	2.06042i	−0.223157	−	0.686807i
$10$	−1.77724			−0.562013
$11$	2.07982	−	2.58348i	0.627089	−	0.778948i
$11$	2.07982	−	2.58348i	0.627089	−	0.778948i
$12$	0.912987			0.263557
$13$	1.67602	+	5.15825i	0.464844	+	1.43064i	0.859179	+	0.511675i	$0.170975\pi$
$13$	1.67602	+	5.15825i	0.464844	+	1.43064i	−0.394336	+	0.918966i	$0.629025\pi$
$14$	4.08354	+	2.96686i	1.09137	+	0.792928i
$15$	1.31271	−	0.953740i	0.338940	−	0.246254i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−0.563182	+	1.73330i	−0.136592	+	0.420386i	−0.995834	−	0.0911826i	$-0.970935\pi$
$17$	−0.563182	+	1.73330i	−0.136592	+	0.420386i	0.859243	+	0.511568i	$0.170935\pi$
$18$	1.75270	−	1.27341i	0.413115	−	0.300146i
$19$	0.809017	+	0.587785i	0.185601	+	0.134847i
$19$	0.809017	+	0.587785i	0.185601	+	0.134847i
$20$	−0.549198	−	1.69026i	−0.122804	−	0.377953i
$21$	−4.60833			−1.00562
$22$	3.09973	+	1.17969i	0.660865	+	0.251510i
$23$	5.61764			1.17136			0.585679	−	0.810543i	$-0.300828\pi$
$23$	5.61764			1.17136			0.585679	+	0.810543i	$0.300828\pi$
$24$	0.282129	+	0.868303i	0.0575893	+	0.177242i
$25$	1.48974	+	1.08236i	0.297947	+	0.216471i
$26$	−4.38787	+	3.18797i	−0.860532	+	0.625213i
$27$	−1.45760	+	4.48605i	−0.280516	+	0.863340i
$28$	−1.55977	+	4.80049i	−0.294769	+	0.907207i
$29$	−1.81205	+	1.31653i	−0.336490	+	0.244474i	−0.743179	−	0.669092i	$-0.766683\pi$
$29$	−1.81205	+	1.31653i	−0.336490	+	0.244474i	0.406690	+	0.913566i	$0.366683\pi$
$30$	1.31271	+	0.953740i	0.239667	+	0.174128i
$31$	0.119445	+	0.367612i	0.0214529	+	0.0660251i	0.961210	−	0.275818i	$-0.0889488\pi$
$31$	0.119445	+	0.367612i	0.0214529	+	0.0660251i	−0.939757	+	0.341843i	$0.888949\pi$
$32$	1.00000			0.176777
$33$	−2.92260	+	0.792100i	−0.508759	+	0.137887i
$34$	−1.82249			−0.312555
$35$	2.77209	+	8.53162i	0.468569	+	1.44211i
$36$	1.75270	+	1.27341i	0.292116	+	0.212235i
$37$	8.16517	−	5.93234i	1.34235	−	0.975271i	0.342992	−	0.939338i	$-0.388560\pi$
$37$	8.16517	−	5.93234i	1.34235	−	0.975271i	0.999354	−	0.0359328i	$-0.0114402\pi$
$38$	−0.309017	+	0.951057i	−0.0501292	+	0.154282i
$39$	1.53018	−	4.70942i	0.245025	−	0.754110i
$40$	1.43782	−	1.04464i	0.227339	−	0.165171i
$41$	−7.51036	−	5.45660i	−1.17292	−	0.852178i	−0.181566	−	0.983379i	$-0.558117\pi$
$41$	−7.51036	−	5.45660i	−1.17292	−	0.852178i	−0.991356	+	0.131201i	$0.958117\pi$
$42$	−1.42405	−	4.38278i	−0.219736	−	0.676278i
$43$	5.45957			0.832576			0.416288	−	0.909233i	$-0.363331\pi$
$43$	5.45957			0.832576			0.416288	+	0.909233i	$0.363331\pi$
$44$	−0.164078	+	3.31256i	−0.0247357	+	0.499388i
$45$	3.85031			0.573970
$46$	1.73595	+	5.34269i	0.255951	+	0.787737i
$47$	−8.74809	−	6.35586i	−1.27604	−	0.927098i	−0.276615	−	0.960981i	$-0.589213\pi$
$47$	−8.74809	−	6.35586i	−1.27604	−	0.927098i	−0.999426	+	0.0338833i	$0.989213\pi$
$48$	−0.738622	+	0.536641i	−0.106611	+	0.0774574i
$49$	5.70988	−	17.5732i	0.815697	−	2.51046i
$50$	−0.569028	+	1.75129i	−0.0804728	+	0.247670i
$51$	1.34613	−	0.978024i	0.188497	−	0.136951i
$52$	−4.38787	−	3.18797i	−0.608488	−	0.442092i
$53$	2.11890	+	6.52132i	0.291054	+	0.895772i	0.984518	+	0.175281i	$0.0560834\pi$
$53$	2.11890	+	6.52132i	0.291054	+	0.895772i	−0.693464	+	0.720491i	$0.743917\pi$
$54$	−4.71691			−0.641890
$55$	3.22451	+	4.93427i	0.434793	+	0.665336i
$56$	−5.04753			−0.674505
$57$	−0.282129	−	0.868303i	−0.0373688	−	0.115009i
$58$	−1.81205	−	1.31653i	−0.237934	−	0.172869i
$59$	−2.99725	+	2.17763i	−0.390209	+	0.283504i	−0.765541	−	0.643387i	$-0.777529\pi$
$59$	−2.99725	+	2.17763i	−0.390209	+	0.283504i	0.375332	+	0.926890i	$0.377529\pi$
$60$	−0.501411	+	1.54318i	−0.0647318	+	0.199224i
$61$	0.893988	−	2.75141i	0.114463	−	0.352282i	−0.877371	−	0.479812i	$-0.840705\pi$
$61$	0.893988	−	2.75141i	0.114463	−	0.352282i	0.991835	+	0.127530i	$0.0407048\pi$
$62$	−0.312710	+	0.227197i	−0.0397142	+	0.0288540i
$63$	−8.84680	−	6.42757i	−1.11459	−	0.809798i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−9.63923			−1.19560
$66$	−1.65646	−	2.53478i	−0.203897	−	0.312010i
$67$	−11.5655			−1.41295			−0.706474	−	0.707739i	$-0.749715\pi$
$67$	−11.5655			−1.41295			−0.706474	+	0.707739i	$0.749715\pi$
$68$	−0.563182	−	1.73330i	−0.0682958	−	0.210193i
$69$	−4.14931	−	3.01465i	−0.499518	−	0.362921i
$70$	−7.25743	+	5.27283i	−0.867429	+	0.630224i
$71$	−0.269698	+	0.830045i	−0.0320073	+	0.0985082i	−0.965784	−	0.259348i	$-0.916492\pi$
$71$	−0.269698	+	0.830045i	−0.0320073	+	0.0985082i	0.933777	+	0.357856i	$0.116492\pi$
$72$	−0.669471	+	2.06042i	−0.0788979	+	0.242823i
$73$	−7.91393	+	5.74981i	−0.926256	+	0.672964i	−0.945073	−	0.326859i	$-0.894010\pi$
$73$	−7.91393	+	5.74981i	−0.926256	+	0.672964i	0.0188176	+	0.999823i	$0.494010\pi$
$74$	8.16517	+	5.93234i	0.949182	+	0.689621i
$75$	−0.519516	−	1.59891i	−0.0599885	−	0.184626i
$76$	−1.00000			−0.114708
$77$	0.828188	−	16.7203i	0.0943808	−	1.90545i
$78$	4.95177			0.560678
$79$	2.87944	+	8.86201i	0.323963	+	0.997054i	0.971907	+	0.235366i	$0.0756290\pi$
$79$	2.87944	+	8.86201i	0.323963	+	0.997054i	−0.647944	+	0.761688i	$0.724371\pi$
$80$	1.43782	+	1.04464i	0.160753	+	0.116794i
$81$	−1.77408	+	1.28895i	−0.197120	+	0.143216i
$82$	2.86870	−	8.82896i	0.316795	−	0.974996i
$83$	−1.32476	+	4.07720i	−0.145411	+	0.447530i	−0.997064	−	0.0765769i	$-0.975601\pi$
$83$	−1.32476	+	4.07720i	−0.145411	+	0.447530i	0.851652	+	0.524107i	$0.175601\pi$
$84$	3.72822	−	2.70871i	0.406782	−	0.295544i
$85$	−2.62042	−	1.90384i	−0.284224	−	0.206501i
$86$	1.68710	+	5.19236i	0.181925	+	0.559906i
$87$	2.04493			0.219239
$88$	−3.20114	+	0.867591i	−0.341242	+	0.0924855i
$89$	−5.60537			−0.594169			−0.297084	−	0.954851i	$-0.596014\pi$
$89$	−5.60537			−0.594169			−0.297084	+	0.954851i	$0.596014\pi$
$90$	1.18981	+	3.66186i	0.125417	+	0.385994i
$91$	22.1479	+	16.0914i	2.32173	+	1.68684i
$92$	−4.54476	+	3.30196i	−0.473824	+	0.344254i
$93$	0.109051	−	0.335626i	0.0113081	−	0.0348027i
$94$	3.34147	−	10.2840i	0.344647	−	1.06071i
$95$	−1.43782	+	1.04464i	−0.147517	+	0.107177i
$96$	−0.738622	−	0.536641i	−0.0753853	−	0.0547706i
$97$	−0.897782	−	2.76309i	−0.0911559	−	0.280549i	0.895077	−	0.445912i	$-0.147121\pi$
$97$	−0.897782	−	2.76309i	−0.0911559	−	0.280549i	−0.986233	+	0.165363i	$0.947121\pi$
$98$	18.4776			1.86652
$99$	−6.71543	−	2.55574i	−0.674926	−	0.256861i
$100$	−1.84141			−0.184141
$101$	−0.164005	−	0.504755i	−0.0163191	−	0.0502250i	0.942565	−	0.334022i	$-0.108406\pi$
$101$	−0.164005	−	0.504755i	−0.0163191	−	0.0502250i	−0.958884	+	0.283797i	$0.908406\pi$
$102$	1.34613	+	0.978024i	0.133287	+	0.0968388i
$103$	2.94394	−	2.13889i	0.290075	−	0.210752i	−0.433225	−	0.901286i	$-0.642624\pi$
$103$	2.94394	−	2.13889i	0.290075	−	0.210752i	0.723300	+	0.690534i	$0.242624\pi$
$104$	1.67602	−	5.15825i	0.164347	−	0.505808i
$105$	2.53088	−	7.78926i	0.246989	−	0.760154i
$106$	−5.54736	+	4.03040i	−0.538808	+	0.391467i
$107$	−7.17457	−	5.21263i	−0.693592	−	0.503924i	0.184247	−	0.982880i	$-0.441015\pi$
$107$	−7.17457	−	5.21263i	−0.693592	−	0.503924i	−0.877839	+	0.478956i	$0.841015\pi$
$108$	−1.45760	−	4.48605i	−0.140258	−	0.431670i
$109$	−2.02691			−0.194143			−0.0970716	−	0.995277i	$-0.530948\pi$
$109$	−2.02691			−0.194143			−0.0970716	+	0.995277i	$0.530948\pi$
$110$	−3.69634	+	4.59146i	−0.352432	+	0.437779i
$111$	−9.21451			−0.874603
$112$	−1.55977	−	4.80049i	−0.147385	−	0.453603i
$113$	−1.30362	−	0.947133i	−0.122634	−	0.0890988i	0.524778	−	0.851239i	$-0.324148\pi$
$113$	−1.30362	−	0.947133i	−0.122634	−	0.0890988i	−0.647412	+	0.762141i	$0.724148\pi$
$114$	0.738622	−	0.536641i	0.0691783	−	0.0502610i
$115$	−3.08519	+	9.49525i	−0.287696	+	0.885436i
$116$	0.692142	−	2.13019i	0.0642638	−	0.197784i
$117$	9.50612	−	6.90660i	0.878841	−	0.638515i
$118$	−2.99725	−	2.17763i	−0.275920	−	0.200467i
$119$	2.84268	+	8.74886i	0.260588	+	0.802007i
$120$	−1.62260			−0.148122
$121$	−2.34871	−	10.7463i	−0.213520	−	0.976939i
$122$	2.89301			0.261920
$123$	2.61909	+	8.06073i	0.236155	+	0.726812i
$124$	−0.312710	−	0.227197i	−0.0280822	−	0.0204029i
$125$	−9.83671	+	7.14679i	−0.879822	+	0.639228i
$126$	3.37918	−	10.4000i	0.301041	−	0.926509i
$127$	4.85384	−	14.9386i	0.430708	−	1.32558i	−0.466713	−	0.884409i	$-0.654562\pi$
$127$	4.85384	−	14.9386i	0.430708	−	1.32558i	0.897421	−	0.441175i	$-0.145438\pi$
$128$	−0.809017	+	0.587785i	−0.0715077	+	0.0519534i
$129$	−4.03256	−	2.92983i	−0.355047	−	0.257957i
$130$	−2.97869	−	9.16745i	−0.261248	−	0.804039i
$131$	13.6488			1.19250			0.596250	−	0.802798i	$-0.296657\pi$
$131$	13.6488			1.19250			0.596250	+	0.802798i	$0.296657\pi$
$132$	1.89885	−	2.35868i	0.165273	−	0.205297i
$133$	5.04753			0.437676
$134$	−3.57393	−	10.9994i	−0.308740	−	0.950205i
$135$	−6.78205	−	4.92745i	−0.583706	−	0.424087i
$136$	1.47443	−	1.07124i	0.126431	−	0.0918577i
$137$	−2.79023	+	8.58745i	−0.238385	+	0.733675i	0.758269	+	0.651942i	$0.226045\pi$
$137$	−2.79023	+	8.58745i	−0.238385	+	0.733675i	−0.996654	+	0.0817330i	$0.973955\pi$
$138$	1.58490	−	4.87781i	0.134915	−	0.415227i
$139$	−8.37929	+	6.08791i	−0.710722	+	0.516370i	−0.883406	−	0.468608i	$-0.844756\pi$
$139$	−8.37929	+	6.08791i	−0.710722	+	0.516370i	0.172685	+	0.984977i	$0.444756\pi$
$140$	−7.25743	−	5.27283i	−0.613365	−	0.445636i
$141$	3.05072	+	9.38916i	0.256917	+	0.790710i
$142$	−0.872761			−0.0732405
$143$	16.8120	+	6.39827i	1.40589	+	0.535050i
$144$	−2.16645			−0.180538
$145$	−1.23010	−	3.78587i	−0.102155	−	0.314399i
$146$	−7.91393	−	5.74981i	−0.654962	−	0.475857i
$147$	−13.6479	+	9.91581i	−1.12566	+	0.817842i
$148$	−3.11882	+	9.59873i	−0.256365	+	0.789011i
$149$	4.39838	−	13.5368i	0.360330	−	1.10898i	−0.592525	−	0.805552i	$-0.701869\pi$
$149$	4.39838	−	13.5368i	0.360330	−	1.10898i	0.952854	−	0.303428i	$-0.0981313\pi$
$150$	1.36011	−	0.988178i	0.111053	−	0.0806844i
$151$	11.5001	+	8.35534i	0.935868	+	0.679948i	0.947423	−	0.319985i	$-0.103678\pi$
$151$	11.5001	+	8.35534i	0.935868	+	0.679948i	−0.0115543	+	0.999933i	$0.503678\pi$
$152$	−0.309017	−	0.951057i	−0.0250646	−	0.0771409i
$153$	3.94835			0.319205
$154$	16.1578	−	4.37919i	1.30204	−	0.352885i
$155$	−0.686958			−0.0551778
$156$	1.53018	+	4.70942i	0.122513	+	0.377055i
$157$	−11.2067	−	8.14217i	−0.894395	−	0.649816i	0.0426251	−	0.999091i	$-0.486428\pi$
$157$	−11.2067	−	8.14217i	−0.894395	−	0.649816i	−0.937020	+	0.349275i	$0.886428\pi$
$158$	−7.53848	+	5.47702i	−0.599729	+	0.435729i
$159$	1.93453	−	5.95388i	0.153418	−	0.472174i
$160$	−0.549198	+	1.69026i	−0.0434179	+	0.133627i
$161$	22.9398	−	16.6668i	1.80791	−	1.31352i
$162$	−1.77408	−	1.28895i	−0.139385	−	0.101269i
$163$	3.37904	+	10.3996i	0.264667	+	0.814561i	0.991770	+	0.128033i	$0.0408663\pi$
$163$	3.37904	+	10.3996i	0.264667	+	0.814561i	−0.727103	+	0.686528i	$0.759134\pi$
$164$	9.28332			0.724906
$165$	0.266233	−	5.37496i	0.0207262	−	0.418440i
$166$	−4.28702			−0.332737
$167$	1.20653	+	3.71331i	0.0933639	+	0.287345i	0.986824	−	0.161798i	$-0.0517294\pi$
$167$	1.20653	+	3.71331i	0.0933639	+	0.287345i	−0.893460	+	0.449143i	$0.851729\pi$
$168$	3.72822	+	2.70871i	0.287638	+	0.208981i
$169$	−13.2813	+	9.64942i	−1.02164	+	0.742263i
$170$	1.00091	−	3.08048i	0.0767663	−	0.236262i
$171$	0.669471	−	2.06042i	0.0511957	−	0.157564i
$172$	−4.41688	+	3.20905i	−0.336784	+	0.244688i
$173$	6.98880	+	5.07766i	0.531349	+	0.386047i	0.820862	−	0.571127i	$-0.193493\pi$
$173$	6.98880	+	5.07766i	0.531349	+	0.386047i	−0.289513	+	0.957174i	$0.593493\pi$
$174$	0.631917	+	1.94484i	0.0479055	+	0.147438i
$175$	9.29460			0.702605
$176$	−1.81433	−	2.77636i	−0.136761	−	0.209276i
$177$	3.38244			0.254240
$178$	−1.73216	−	5.33103i	−0.129831	−	0.399577i
$179$	5.04764	+	3.66733i	0.377279	+	0.274109i	0.760223	−	0.649663i	$-0.225090\pi$
$179$	5.04764	+	3.66733i	0.377279	+	0.274109i	−0.382944	+	0.923772i	$0.625090\pi$
$180$	−3.11497	+	2.26316i	−0.232176	+	0.168686i
$181$	−8.08218	+	24.8744i	−0.600744	+	1.84890i	−0.0769840	+	0.997032i	$0.524529\pi$
$181$	−8.08218	+	24.8744i	−0.600744	+	1.84890i	−0.523760	+	0.851866i	$0.675471\pi$
$182$	−8.45975	+	26.0364i	−0.627078	+	1.92995i
$183$	−2.13684	+	1.55250i	−0.157960	+	0.114764i
$184$	−4.54476	−	3.30196i	−0.335044	−	0.243424i
$185$	5.54289	+	17.0593i	0.407521	+	1.25422i
$186$	0.352898			0.0258757
$187$	3.30661	+	5.05991i	0.241804	+	0.370017i
$188$	10.8132			0.788636
$189$	7.35730	+	22.6435i	0.535165	+	1.64707i
$190$	−1.43782	−	1.04464i	−0.104310	−	0.0757859i
$191$	−21.0333	+	15.2816i	−1.52191	+	1.10573i	−0.561383	+	0.827556i	$0.689731\pi$
$191$	−21.0333	+	15.2816i	−1.52191	+	1.10573i	−0.960529	+	0.278178i	$0.910269\pi$
$192$	0.282129	−	0.868303i	0.0203609	−	0.0626643i
$193$	2.82992	−	8.70961i	0.203702	−	0.626931i	−0.796062	−	0.605215i	$-0.793087\pi$
$193$	2.82992	−	8.70961i	0.203702	−	0.626931i	0.999764	−	0.0217160i	$-0.00691297\pi$
$194$	2.35042	−	1.70768i	0.168751	−	0.122604i
$195$	7.11975	+	5.17280i	0.509856	+	0.370432i
$196$	5.70988	+	17.5732i	0.407849	+	1.25523i
$197$	−19.5680			−1.39416			−0.697080	−	0.716994i	$-0.745518\pi$
$197$	−19.5680			−1.39416			−0.697080	+	0.716994i	$0.745518\pi$
$198$	0.355467	−	7.17652i	0.0252620	−	0.510013i
$199$	−14.8418			−1.05211			−0.526055	−	0.850451i	$-0.676329\pi$
$199$	−14.8418			−1.05211			−0.526055	+	0.850451i	$0.676329\pi$
$200$	−0.569028	−	1.75129i	−0.0402364	−	0.123835i
$201$	8.54252	+	6.20650i	0.602543	+	0.437773i
$202$	0.429370	−	0.311956i	0.0302104	−	0.0219491i
$203$	−3.49361	+	10.7522i	−0.245203	+	0.754658i
$204$	−0.514178	+	1.58248i	−0.0359996	+	0.110796i
$205$	13.3477	−	9.69769i	0.932246	−	0.677316i
$206$	2.94394	+	2.13889i	0.205114	+	0.149024i
$207$	−3.76085	−	11.5747i	−0.261397	−	0.804497i
$208$	5.42371			0.376066
$209$	3.20114	−	0.867591i	0.221427	−	0.0600125i
$210$	8.19012			0.565172
$211$	−5.44664	−	16.7630i	−0.374962	−	1.15402i	−0.943504	−	0.331361i	$-0.892492\pi$
$211$	−5.44664	−	16.7630i	−0.374962	−	1.15402i	0.568542	−	0.822654i	$-0.307508\pi$
$212$	−5.54736	−	4.03040i	−0.380995	−	0.276809i
$213$	0.644641	−	0.468359i	0.0441701	−	0.0320914i
$214$	2.74044	−	8.43421i	0.187333	−	0.576551i
$215$	−2.99838	+	9.22807i	−0.204488	+	0.629349i
$216$	3.81606	−	2.77253i	0.259650	−	0.188647i
$217$	1.57841	+	1.14678i	0.107150	+	0.0778488i
$218$	−0.626351	−	1.92771i	−0.0424218	−	0.130561i
$219$	8.93099			0.603500
$220$	−5.50897	−	2.09659i	−0.371415	−	0.141352i
$221$	−9.88467			−0.664915
$222$	−2.84744	−	8.76352i	−0.191108	−	0.588169i
$223$	−8.20301	−	5.95983i	−0.549314	−	0.399100i	0.278218	−	0.960518i	$-0.410256\pi$
$223$	−8.20301	−	5.95983i	−0.549314	−	0.399100i	−0.827533	+	0.561418i	$0.810256\pi$
$224$	4.08354	−	2.96686i	0.272843	−	0.198232i
$225$	1.23277	−	3.79409i	0.0821849	−	0.252939i
$226$	0.497937	−	1.53249i	0.0331223	−	0.101940i
$227$	−7.41833	+	5.38973i	−0.492372	+	0.357729i	−0.806096	−	0.591785i	$-0.798423\pi$
$227$	−7.41833	+	5.38973i	−0.492372	+	0.357729i	0.313724	+	0.949514i	$0.398423\pi$
$228$	0.738622	+	0.536641i	0.0489165	+	0.0355399i
$229$	−0.141593	−	0.435778i	−0.00935671	−	0.0287970i	0.946269	−	0.323380i	$-0.104819\pi$
$229$	−0.141593	−	0.435778i	−0.00935671	−	0.0287970i	−0.955626	+	0.294583i	$0.904819\pi$
$230$	−9.98389			−0.658318
$231$	−9.58449	+	11.9055i	−0.630613	+	0.783326i
$232$	2.23982			0.147051
$233$	1.80411	+	5.55248i	0.118191	+	0.363755i	0.992599	−	0.121436i	$-0.0387500\pi$
$233$	1.80411	+	5.55248i	0.118191	+	0.363755i	−0.874408	+	0.485191i	$0.838750\pi$
$234$	9.50612	+	6.90660i	0.621434	+	0.451499i
$235$	15.5475	−	11.2959i	1.01420	−	0.736863i
$236$	1.14485	−	3.52348i	0.0745233	−	0.229359i
$237$	2.62889	−	8.09091i	0.170765	−	0.525561i
$238$	−7.44222	+	5.40709i	−0.482408	+	0.350490i
$239$	−6.22582	−	4.52333i	−0.402715	−	0.292590i	0.367931	−	0.929853i	$-0.380066\pi$
$239$	−6.22582	−	4.52333i	−0.402715	−	0.292590i	−0.770646	+	0.637263i	$0.780066\pi$
$240$	−0.501411	−	1.54318i	−0.0323659	−	0.0996120i
$241$	−11.2195			−0.722714			−0.361357	−	0.932428i	$-0.617686\pi$
$241$	−11.2195			−0.722714			−0.361357	+	0.932428i	$0.617686\pi$
$242$	9.49457	−	5.55456i	0.610334	−	0.357061i
$243$	16.1528			1.03620
$244$	0.893988	+	2.75141i	0.0572317	+	0.176141i
$245$	26.5674	+	19.3023i	1.69733	+	1.23318i
$246$	−6.85687	+	4.98181i	−0.437178	+	0.317628i
$247$	−1.67602	+	5.15825i	−0.106642	+	0.328212i
$248$	0.119445	−	0.367612i	0.00758474	−	0.0233434i
$249$	3.16649	−	2.30059i	0.200668	−	0.145794i
$250$	−9.83671	−	7.14679i	−0.622128	−	0.452003i
$251$	−0.910181	−	2.80125i	−0.0574501	−	0.176813i	0.918214	−	0.396086i	$-0.129632\pi$
$251$	−0.910181	−	2.80125i	−0.0574501	−	0.176813i	−0.975664	+	0.219272i	$0.929632\pi$
$252$	10.9352			0.688856
$253$	11.6837	−	14.5130i	0.734545	−	0.912427i
$254$	15.7073			0.985566
$255$	0.913818	+	2.81244i	0.0572255	+	0.176122i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−17.1415	+	12.4541i	−1.06926	+	0.776863i	−0.975779	−	0.218758i	$-0.929799\pi$
$257$	−17.1415	+	12.4541i	−1.06926	+	0.776863i	−0.0934807	+	0.995621i	$0.529799\pi$
$258$	1.54030	−	4.74056i	0.0958949	−	0.295134i
$259$	15.7423	−	48.4499i	0.978181	−	3.01053i
$260$	7.79830	−	5.66580i	0.483630	−	0.351378i
$261$	3.92573	+	2.85221i	0.242996	+	0.176547i
$262$	4.21771	+	12.9808i	0.260571	+	0.801955i
$263$	3.78559			0.233430			0.116715	−	0.993165i	$-0.462764\pi$
$263$	3.78559			0.233430			0.116715	+	0.993165i	$0.462764\pi$
$264$	2.83002	+	1.07704i	0.174175	+	0.0662871i
$265$	−12.1864			−0.748604
$266$	1.55977	+	4.80049i	0.0956358	+	0.294337i
$267$	4.14026	+	3.00807i	0.253380	+	0.184091i
$268$	9.35667	−	6.79802i	0.571549	−	0.415255i
$269$	−8.97391	+	27.6188i	−0.547149	+	1.68395i	0.168677	+	0.985671i	$0.446051\pi$
$269$	−8.97391	+	27.6188i	−0.547149	+	1.68395i	−0.715825	+	0.698279i	$0.753949\pi$
$270$	2.59051	−	7.97278i	0.157654	−	0.485208i
$271$	−13.3925	+	9.73022i	−0.813536	+	0.591069i	−0.914854	−	0.403785i	$-0.867694\pi$
$271$	−13.3925	+	9.73022i	−0.813536	+	0.591069i	0.101317	+	0.994854i	$0.467694\pi$
$272$	1.47443	+	1.07124i	0.0894004	+	0.0649532i
$273$	−7.72364	−	23.7709i	−0.467456	−	1.43868i
$274$	−9.02937			−0.545484
$275$	5.89462	−	1.59760i	0.355459	−	0.0963386i
$276$	5.12883			0.308719
$277$	6.46644	+	19.9017i	0.388531	+	1.19577i	0.933886	+	0.357570i	$0.116395\pi$
$277$	6.46644	+	19.9017i	0.388531	+	1.19577i	−0.545356	+	0.838205i	$0.683605\pi$
$278$	−8.37929	−	6.08791i	−0.502556	−	0.365128i
$279$	0.677471	−	0.492212i	0.0405592	−	0.0294680i
$280$	2.77209	−	8.53162i	0.165664	−	0.509862i
$281$	−2.66830	+	8.21218i	−0.159177	+	0.489898i	−0.998560	−	0.0536431i	$-0.982917\pi$
$281$	−2.66830	+	8.21218i	−0.159177	+	0.489898i	0.839383	+	0.543541i	$0.182917\pi$
$282$	−7.98690	+	5.80282i	−0.475613	+	0.345553i
$283$	−5.10673	−	3.71026i	−0.303563	−	0.220552i	0.425566	−	0.904927i	$-0.360075\pi$
$283$	−5.10673	−	3.71026i	−0.303563	−	0.220552i	−0.729130	+	0.684375i	$0.760075\pi$
$284$	−0.269698	−	0.830045i	−0.0160036	−	0.0492541i
$285$	1.62260			0.0961144
$286$	−0.889910	+	17.9664i	−0.0526215	+	1.06237i
$287$	−46.8578			−2.76593
$288$	−0.669471	−	2.06042i	−0.0394490	−	0.121411i
$289$	11.0662	+	8.04003i	0.650950	+	0.472943i
$290$	3.22045	−	2.33980i	0.189112	−	0.137398i
$291$	−0.819663	+	2.52266i	−0.0480495	+	0.147881i
$292$	3.02285	−	9.30338i	0.176899	−	0.544439i
$293$	10.2558	−	7.45127i	0.599150	−	0.435308i	−0.246427	−	0.969161i	$-0.579257\pi$
$293$	10.2558	−	7.45127i	0.599150	−	0.435308i	0.845577	+	0.533854i	$0.179257\pi$
$294$	−13.6479	−	9.91581i	−0.795964	−	0.578302i
$295$	−2.03467	−	6.26208i	−0.118463	−	0.364592i
$296$	−10.0927			−0.586627
$297$	8.55805	+	13.0958i	0.496588	+	0.759898i
$298$	14.2335			0.824523
$299$	9.41526	+	28.9772i	0.544498	+	1.67579i
$300$	1.36011	+	0.988178i	0.0785260	+	0.0570525i
$301$	22.2943	−	16.1978i	1.28502	−	0.933625i
$302$	−4.39266	+	13.5192i	−0.252769	+	0.777944i
$303$	−0.149734	+	0.460835i	−0.00860202	+	0.0264743i
$304$	0.809017	−	0.587785i	0.0464003	−	0.0337118i
$305$	4.15962	+	3.02214i	0.238179	+	0.173047i
$306$	1.22011	+	3.75510i	0.0697489	+	0.214665i
$307$	26.6423			1.52056			0.760279	−	0.649597i	$-0.225062\pi$
$307$	26.6423			1.52056			0.760279	+	0.649597i	$0.225062\pi$
$308$	9.15791	+	14.0138i	0.521820	+	0.798509i
$309$	−3.32227			−0.188998
$310$	−0.212282	−	0.653336i	−0.0120568	−	0.0371070i
$311$	20.2935	+	14.7441i	1.15074	+	0.836059i	0.988579	−	0.150706i	$-0.0481545\pi$
$311$	20.2935	+	14.7441i	1.15074	+	0.836059i	0.162158	+	0.986765i	$0.448155\pi$
$312$	−4.00607	+	2.91058i	−0.226799	+	0.164779i
$313$	10.5477	−	32.4624i	0.596189	−	1.83488i	0.0474744	−	0.998872i	$-0.484883\pi$
$313$	10.5477	−	32.4624i	0.596189	−	1.83488i	0.548715	−	0.836010i	$-0.315117\pi$
$314$	4.28059	−	13.1743i	0.241568	−	0.743469i
$315$	15.7229	−	11.4233i	0.885884	−	0.643633i
$316$	−7.53848	−	5.47702i	−0.424072	−	0.308107i
$317$	−9.32396	−	28.6962i	−0.523686	−	1.61174i	−0.766900	−	0.641767i	$-0.778202\pi$
$317$	−9.32396	−	28.6962i	−0.523686	−	1.61174i	0.243214	−	0.969973i	$-0.421798\pi$
$318$	6.26028			0.351059
$319$	−0.367505	+	7.41954i	−0.0205763	+	0.415415i
$320$	−1.77724			−0.0993508
$321$	2.50199	+	7.70033i	0.139647	+	0.429790i
$322$	22.9398	+	16.6668i	1.27839	+	0.928802i
$323$	−1.47443	+	1.07124i	−0.0820394	+	0.0596051i
$324$	0.677639	−	2.08556i	0.0376466	−	0.115864i
$325$	−3.08624	+	9.49848i	−0.171194	+	0.526881i
$326$	−8.84645	+	6.42732i	−0.489959	+	0.355976i
$327$	1.49712	+	1.08772i	0.0827912	+	0.0601513i
$328$	2.86870	+	8.82896i	0.158398	+	0.487498i
$329$	−54.5801			−3.00910
$330$	5.19416	−	1.40775i	0.285929	−	0.0774942i
$331$	10.7721			0.592091			0.296045	−	0.955174i	$-0.404332\pi$
$331$	10.7721			0.592091			0.296045	+	0.955174i	$0.404332\pi$
$332$	−1.32476	−	4.07720i	−0.0727057	−	0.223765i
$333$	−17.6895	−	12.8521i	−0.969377	−	0.704293i
$334$	−3.15873	+	2.29495i	−0.172838	+	0.125574i
$335$	6.35173	−	19.5486i	0.347032	−	1.06806i
$336$	−1.42405	+	4.38278i	−0.0776884	+	0.239100i
$337$	3.93485	−	2.85883i	0.214345	−	0.155731i	−0.475433	−	0.879752i	$-0.657708\pi$
$337$	3.93485	−	2.85883i	0.214345	−	0.155731i	0.689777	+	0.724022i	$0.257708\pi$
$338$	−13.2813	−	9.64942i	−0.722407	−	0.524859i
$339$	0.454610	+	1.39915i	0.0246910	+	0.0759912i
$340$	3.23901			0.175660
$341$	1.19814	+	0.455985i	0.0648830	+	0.0246930i
$342$	2.16645			0.117148
$343$	−17.9024	−	55.0979i	−0.966638	−	2.97501i
$344$	−4.41688	−	3.20905i	−0.238142	−	0.173021i
$345$	7.37433	−	5.35776i	0.397020	−	0.288452i
$346$	−2.66948	+	8.21583i	−0.143512	+	0.441686i
$347$	2.72037	−	8.37245i	0.146037	−	0.449456i	−0.851106	−	0.524994i	$-0.824067\pi$
$347$	2.72037	−	8.37245i	0.146037	−	0.449456i	0.997143	+	0.0755380i	$0.0240674\pi$
$348$	−1.65438	+	1.20198i	−0.0886841	+	0.0644328i
$349$	−18.0670	−	13.1264i	−0.967103	−	0.702641i	−0.0123134	−	0.999924i	$-0.503920\pi$
$349$	−18.0670	−	13.1264i	−0.967103	−	0.702641i	−0.954789	+	0.297283i	$0.903920\pi$
$350$	2.87219	+	8.83969i	0.153525	+	0.472501i
$351$	−25.5831			−1.36553
$352$	2.07982	−	2.58348i	0.110855	−	0.137700i
$353$	−7.98769			−0.425142			−0.212571	−	0.977146i	$-0.568184\pi$
$353$	−7.98769			−0.425142			−0.212571	+	0.977146i	$0.568184\pi$
$354$	1.04523	+	3.21690i	0.0555535	+	0.170976i
$355$	−1.25487	−	0.911718i	−0.0666017	−	0.0483889i
$356$	4.53484	−	3.29476i	0.240346	−	0.174622i
$357$	2.59533	−	7.98760i	0.137359	−	0.422749i
$358$	−1.92803	+	5.93386i	−0.101899	+	0.313614i
$359$	21.2479	−	15.4375i	1.12142	−	0.814761i	0.136999	−	0.990571i	$-0.456254\pi$
$359$	21.2479	−	15.4375i	1.12142	−	0.814761i	0.984424	+	0.175810i	$0.0562544\pi$
$360$	−3.11497	−	2.26316i	−0.164173	−	0.119279i
$361$	0.309017	+	0.951057i	0.0162641	+	0.0500556i
$362$	−26.1545			−1.37465
$363$	−4.03210	+	9.19789i	−0.211630	+	0.482764i
$364$	−27.3763			−1.43491
$365$	−5.37234	−	16.5344i	−0.281201	−	0.865448i
$366$	−2.13684	−	1.55250i	−0.111694	−	0.0811507i
$367$	12.5456	−	9.11489i	0.654873	−	0.475793i	−0.210054	−	0.977690i	$-0.567364\pi$
$367$	12.5456	−	9.11489i	0.654873	−	0.475793i	0.864928	+	0.501896i	$0.167364\pi$
$368$	1.73595	−	5.34269i	0.0904924	−	0.278507i
$369$	−6.21492	+	19.1275i	−0.323536	+	0.995740i
$370$	−14.5115	+	10.5432i	−0.754416	+	0.548115i
$371$	28.0005	+	20.3435i	1.45371	+	1.05618i
$372$	0.109051	+	0.335626i	0.00565405	+	0.0174014i
$373$	−17.4626			−0.904179			−0.452090	−	0.891972i	$-0.649321\pi$
$373$	−17.4626			−0.904179			−0.452090	+	0.891972i	$0.649321\pi$
$374$	−3.79046	+	4.70837i	−0.196000	+	0.243464i
$375$	11.1009			0.573246
$376$	3.34147	+	10.2840i	0.172323	+	0.530357i
$377$	−9.82804	−	7.14049i	−0.506170	−	0.367754i
$378$	−19.2617	+	13.9944i	−0.990713	+	0.719795i
$379$	−9.78332	+	30.1100i	−0.502535	+	1.54664i	0.302339	+	0.953200i	$0.402232\pi$
$379$	−9.78332	+	30.1100i	−0.502535	+	1.54664i	−0.804875	+	0.593445i	$0.797768\pi$
$380$	0.549198	−	1.69026i	0.0281732	−	0.0867083i
$381$	−11.6018	+	8.42920i	−0.594378	+	0.431841i
$382$	−21.0333	−	15.2816i	−1.07615	−	0.781872i
$383$	−1.88465	−	5.80035i	−0.0963010	−	0.296384i	0.891290	−	0.453435i	$-0.149801\pi$
$383$	−1.88465	−	5.80035i	−0.0963010	−	0.296384i	−0.987591	+	0.157051i	$0.949801\pi$
$384$	0.912987			0.0465907
$385$	27.8067	+	10.5826i	1.41716	+	0.539338i
$386$	9.15782			0.466121
$387$	−3.65502	−	11.2490i	−0.185795	−	0.571819i
$388$	2.35042	+	1.70768i	0.119325	+	0.0866944i
$389$	25.9067	−	18.8223i	1.31352	−	0.954329i	0.313533	−	0.949577i	$-0.398487\pi$
$389$	25.9067	−	18.8223i	1.31352	−	0.954329i	0.999989	−	0.00475184i	$-0.00151256\pi$
$390$	−2.71950	+	8.36977i	−0.137707	+	0.423820i
$391$	−3.16375	+	9.73702i	−0.159998	+	0.492422i
$392$	−14.9487	+	10.8608i	−0.755021	+	0.548555i
$393$	−10.0813	−	7.32450i	−0.508535	−	0.369472i
$394$	−6.04683	−	18.6102i	−0.304635	−	0.937570i
$395$	−16.5605			−0.833247
$396$	6.93512	−	1.87960i	0.348503	−	0.0944533i
$397$	10.0101			0.502395			0.251197	−	0.967936i	$-0.419176\pi$
$397$	10.0101			0.502395			0.251197	+	0.967936i	$0.419176\pi$
$398$	−4.58638	−	14.1154i	−0.229894	−	0.707542i
$399$	−3.72822	−	2.70871i	−0.186644	−	0.135605i
$400$	1.48974	−	1.08236i	0.0744868	−	0.0541178i
$401$	−1.64121	+	5.05111i	−0.0819579	+	0.252241i	−0.983636	−	0.180168i	$-0.942336\pi$
$401$	−1.64121	+	5.05111i	−0.0819579	+	0.252241i	0.901678	+	0.432408i	$0.142336\pi$
$402$	−3.26295	+	10.0423i	−0.162741	+	0.500866i
$403$	−1.69605	+	1.23225i	−0.0844861	+	0.0613827i
$404$	0.429370	+	0.311956i	0.0213620	+	0.0155204i
$405$	−1.20433	−	3.70654i	−0.0598435	−	0.184179i
$406$	−11.3056			−0.561085
$407$	1.65599	−	33.4327i	0.0820844	−	1.65720i
$408$	−1.66391			−0.0823760
$409$	5.72979	+	17.6345i	0.283320	+	0.871969i	0.986897	+	0.161350i	$0.0515849\pi$
$409$	5.72979	+	17.6345i	0.283320	+	0.871969i	−0.703577	+	0.710619i	$0.748415\pi$
$410$	13.3477	+	9.69769i	0.659197	+	0.478935i
$411$	6.66930	−	4.84553i	0.328972	−	0.239012i
$412$	−1.12448	+	3.46080i	−0.0553993	+	0.170502i
$413$	−5.77866	+	17.7849i	−0.284349	+	0.875137i
$414$	9.84602	−	7.15355i	0.483906	−	0.351578i
$415$	−6.16395	−	4.47837i	−0.302577	−	0.219835i
$416$	1.67602	+	5.15825i	0.0821735	+	0.252904i
$417$	9.45615			0.463069
$418$	1.81433	+	2.77636i	0.0887420	+	0.135796i
$419$	11.5438			0.563953			0.281977	−	0.959421i	$-0.409010\pi$
$419$	11.5438			0.563953			0.281977	+	0.959421i	$0.409010\pi$
$420$	2.53088	+	7.78926i	0.123495	+	0.380077i
$421$	−27.2865	−	19.8248i	−1.32986	−	0.966201i	−0.999752	−	0.0222580i	$-0.992914\pi$
$421$	−27.2865	−	19.8248i	−1.32986	−	0.966201i	−0.330109	−	0.943943i	$-0.607086\pi$
$422$	14.2595	−	10.3601i	0.694141	−	0.504323i
$423$	−7.23915	+	22.2798i	−0.351979	+	1.08328i
$424$	2.11890	−	6.52132i	0.102903	−	0.316703i
$425$	−2.71504	+	1.97259i	−0.131699	+	0.0956846i
$426$	0.644641	+	0.468359i	0.0312329	+	0.0226921i
$427$	−4.51243	−	13.8878i	−0.218372	−	0.672080i
$428$	8.86825			0.428663
$429$	−8.98417	−	13.7479i	−0.433760	−	0.663756i
$430$	−9.70297			−0.467919
$431$	−3.09983	−	9.54030i	−0.149314	−	0.459540i	0.848227	−	0.529633i	$-0.177670\pi$
$431$	−3.09983	−	9.54030i	−0.149314	−	0.459540i	−0.997540	+	0.0700930i	$0.977670\pi$
$432$	3.81606	+	2.77253i	0.183600	+	0.133393i
$433$	6.39715	−	4.64780i	0.307427	−	0.223359i	−0.423364	−	0.905959i	$-0.639151\pi$
$433$	6.39715	−	4.64780i	0.307427	−	0.223359i	0.730792	+	0.682600i	$0.239151\pi$
$434$	−0.602900	+	1.85554i	−0.0289401	+	0.0890685i
$435$	−1.12307	+	3.45645i	−0.0538470	+	0.165724i
$436$	1.63981	−	1.19139i	0.0785326	−	0.0570572i
$437$	4.54476	+	3.30196i	0.217406	+	0.157954i
$438$	2.75983	+	8.49387i	0.131870	+	0.405853i
$439$	25.7405			1.22853			0.614263	−	0.789102i	$-0.289453\pi$
$439$	25.7405			1.22853			0.614263	+	0.789102i	$0.289453\pi$
$440$	0.291606	−	5.88722i	0.0139018	−	0.280662i
$441$	−40.0308			−1.90623
$442$	−3.05453	−	9.40088i	−0.145289	−	0.447154i
$443$	19.5800	+	14.2257i	0.930276	+	0.675885i	0.946060	−	0.323990i	$-0.105025\pi$
$443$	19.5800	+	14.2257i	0.930276	+	0.675885i	−0.0157845	+	0.999875i	$0.505025\pi$
$444$	7.45470	−	5.41615i	0.353784	−	0.257039i
$445$	3.07846	−	9.47452i	0.145933	−	0.449135i
$446$	3.13327	−	9.64321i	0.148365	−	0.456619i
$447$	−10.5132	+	7.63826i	−0.497255	+	0.361277i
$448$	4.08354	+	2.96686i	0.192929	+	0.140171i
$449$	11.2812	+	34.7200i	0.532393	+	1.63854i	0.749215	+	0.662327i	$0.230431\pi$
$449$	11.2812	+	34.7200i	0.532393	+	1.63854i	−0.216822	+	0.976211i	$0.569569\pi$
$450$	3.98934			0.188059
$451$	−29.7172	+	8.05413i	−1.39933	+	0.379254i
$452$	1.61136			0.0757919
$453$	−4.01045	−	12.3429i	−0.188427	−	0.579919i
$454$	−7.41833	−	5.38973i	−0.348159	−	0.252953i
$455$	−39.3622	+	28.5983i	−1.84533	+	1.34071i
$456$	−0.282129	+	0.868303i	−0.0132119	+	0.0406620i
$457$	4.87048	−	14.9898i	0.227831	−	0.701193i	−0.770161	−	0.637850i	$-0.779824\pi$
$457$	4.87048	−	14.9898i	0.227831	−	0.701193i	0.997992	−	0.0633425i	$-0.0201760\pi$
$458$	0.370695	−	0.269325i	0.0173214	−	0.0125847i
$459$	−6.95474	−	5.05292i	−0.324620	−	0.235850i
$460$	−3.08519	−	9.49525i	−0.143848	−	0.442718i
$461$	6.61141			0.307924			0.153962	−	0.988077i	$-0.450797\pi$
$461$	6.61141			0.307924			0.153962	+	0.988077i	$0.450797\pi$
$462$	−14.2846	−	5.43638i	−0.664580	−	0.252923i
$463$	−32.4747			−1.50923			−0.754614	−	0.656169i	$-0.772176\pi$
$463$	−32.4747			−1.50923			−0.754614	+	0.656169i	$0.772176\pi$
$464$	0.692142	+	2.13019i	0.0321319	+	0.0988918i
$465$	0.507403	+	0.368650i	0.0235302	+	0.0170957i
$466$	−4.72322	+	3.43162i	−0.218799	+	0.158967i
$467$	11.7610	−	36.1967i	0.544236	−	1.67498i	−0.178565	−	0.983928i	$-0.557146\pi$
$467$	11.7610	−	36.1967i	0.544236	−	1.67498i	0.722801	−	0.691057i	$-0.242854\pi$
$468$	−3.63101	+	11.1751i	−0.167844	+	0.516570i
$469$	−47.2281	+	34.3132i	−2.18079	+	1.58444i
$470$	15.5475	+	11.2959i	0.717151	+	0.521041i
$471$	3.90813	+	12.0280i	0.180077	+	0.554220i
$472$	3.70481			0.170528
$473$	11.3549	−	14.1047i	0.522099	−	0.648533i
$474$	8.50728			0.390752
$475$	0.569028	+	1.75129i	0.0261088	+	0.0803547i
$476$	−7.44222	−	5.40709i	−0.341114	−	0.247834i
$477$	12.0181	−	8.73167i	0.550271	−	0.399796i
$478$	2.37805	−	7.31890i	0.108770	−	0.334758i
$479$	9.29807	−	28.6165i	0.424840	−	1.30752i	−0.478308	−	0.878192i	$-0.658750\pi$
$479$	9.29807	−	28.6165i	0.424840	−	1.30752i	0.903148	−	0.429330i	$-0.141250\pi$
$480$	1.31271	−	0.953740i	0.0599167	−	0.0435321i
$481$	44.2855	+	32.1753i	2.01924	+	1.46707i
$482$	−3.46703	−	10.6704i	−0.157919	−	0.486024i
$483$	−25.8879			−1.17794
$484$	8.21668	+	7.31342i	0.373486	+	0.332428i
$485$	5.16339			0.234457
$486$	4.99149	+	15.3622i	0.226419	+	0.696845i
$487$	2.17944	+	1.58346i	0.0987599	+	0.0717532i	0.636069	−	0.771632i	$-0.280559\pi$
$487$	2.17944	+	1.58346i	0.0987599	+	0.0717532i	−0.537309	+	0.843385i	$0.680559\pi$
$488$	−2.34049	+	1.70047i	−0.105949	+	0.0769765i
$489$	3.08502	−	9.49472i	0.139510	−	0.429366i
$490$	−10.1478	+	31.2318i	−0.458432	+	1.41091i
$491$	−22.5578	+	16.3892i	−1.01802	+	0.739635i	−0.965876	−	0.259004i	$-0.916606\pi$
$491$	−22.5578	+	16.3892i	−1.01802	+	0.739635i	−0.0521445	+	0.998640i	$0.516606\pi$
$492$	−6.85687	−	4.98181i	−0.309131	−	0.224597i
$493$	−1.26143	−	3.88227i	−0.0568117	−	0.174849i
$494$	−5.42371			−0.244024
$495$	8.00795	−	9.94719i	0.359930	−	0.447093i
$496$	0.386531			0.0173557
$497$	1.36131	+	4.18968i	0.0610630	+	0.187933i
$498$	3.16649	+	2.30059i	0.141894	+	0.103092i
$499$	−16.9919	+	12.3453i	−0.760662	+	0.552653i	−0.899113	−	0.437716i	$-0.855787\pi$
$499$	−16.9919	+	12.3453i	−0.760662	+	0.552653i	0.138452	+	0.990369i	$0.455787\pi$
$500$	3.75729	−	11.5637i	0.168031	−	0.517146i
$501$	1.10154	−	3.39021i	0.0492134	−	0.151463i
$502$	2.38289	−	1.73127i	0.106353	−	0.0772703i
$503$	8.63349	+	6.27260i	0.384948	+	0.279681i	0.763382	−	0.645947i	$-0.223537\pi$
$503$	8.63349	+	6.27260i	0.384948	+	0.279681i	−0.378434	+	0.925628i	$0.623537\pi$
$504$	3.37918	+	10.4000i	0.150520	+	0.463254i
$505$	0.943237			0.0419735
$506$	17.4132	+	6.62705i	0.774110	+	0.294608i
$507$	14.9881			0.665646
$508$	4.85384	+	14.9386i	0.215354	+	0.662792i
$509$	11.1296	+	8.08614i	0.493312	+	0.358412i	0.806457	−	0.591293i	$-0.201382\pi$
$509$	11.1296	+	8.08614i	0.493312	+	0.358412i	−0.313145	+	0.949705i	$0.601382\pi$
$510$	−2.39241	+	1.73818i	−0.105938	+	0.0769681i
$511$	−15.2579	+	46.9591i	−0.674972	+	2.07735i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	−3.81606	+	2.77253i	−0.168483	+	0.122410i
$514$	−17.1415	−	12.4541i	−0.756081	−	0.549325i
$515$	1.99848	+	6.15068i	0.0880635	+	0.271031i
$516$	4.98452			0.219431
$517$	−34.6147	+	9.38147i	−1.52235	+	0.412596i
$518$	50.9432			2.23832
$519$	−2.43721	−	7.50095i	−0.106981	−	0.329255i
$520$	7.79830	+	5.66580i	0.341978	+	0.248462i
$521$	4.63765	−	3.36945i	0.203179	−	0.147618i	−0.481543	−	0.876422i	$-0.659924\pi$
$521$	4.63765	−	3.36945i	0.203179	−	0.147618i	0.684722	+	0.728804i	$0.259924\pi$
$522$	−1.49949	+	4.61497i	−0.0656311	+	0.201992i
$523$	4.23744	−	13.0415i	0.185290	−	0.570265i	−0.814663	−	0.579935i	$-0.803078\pi$
$523$	4.23744	−	13.0415i	0.185290	−	0.570265i	0.999953	+	0.00967003i	$0.00307811\pi$
$524$	−11.0421	+	8.02256i	−0.482377	+	0.350467i
$525$	−6.86520	−	4.98786i	−0.299622	−	0.217688i
$526$	1.16981	+	3.60031i	0.0510063	+	0.156981i
$527$	−0.704450			−0.0306863
$528$	−0.149801	+	3.02433i	−0.00651926	+	0.131617i
$529$	8.55784			0.372080
$530$	−3.76580	−	11.5900i	−0.163576	−	0.503435i
$531$	6.49341	+	4.71774i	0.281790	+	0.204732i
$532$	−4.08354	+	2.96686i	−0.177044	+	0.128630i
$533$	15.5590	−	47.8857i	0.673935	−	2.07416i
$534$	−1.58144	+	4.86716i	−0.0684355	+	0.210623i
$535$	12.7509	−	9.26409i	0.551271	−	0.400522i
$536$	9.35667	+	6.79802i	0.404146	+	0.293630i
$537$	−1.76027	−	5.41754i	−0.0759611	−	0.233784i
$538$	−29.0402			−1.25201
$539$	−33.5245	−	51.3004i	−1.44400	−	2.20967i
$540$	8.38308			0.360750
$541$	−3.08597	−	9.49763i	−0.132676	−	0.408335i	0.862545	−	0.505980i	$-0.168869\pi$
$541$	−3.08597	−	9.49763i	−0.132676	−	0.408335i	−0.995221	+	0.0976449i	$0.968869\pi$
$542$	−13.3925	−	9.73022i	−0.575257	−	0.417949i
$543$	19.3183	−	14.0356i	0.829027	−	0.602323i
$544$	−0.563182	+	1.73330i	−0.0241462	+	0.0743144i
$545$	1.11318	−	3.42601i	0.0476832	−	0.146754i
$546$	20.2208	−	14.6912i	0.865369	−	0.628727i
$547$	0.927311	+	0.673731i	0.0396489	+	0.0288066i	0.607433	−	0.794371i	$-0.292199\pi$
$547$	0.927311	+	0.673731i	0.0396489	+	0.0288066i	−0.567784	+	0.823177i	$0.692199\pi$
$548$	−2.79023	−	8.58745i	−0.119193	−	0.366837i
$549$	−6.26757			−0.267493
$550$	3.34094	+	5.11244i	0.142458	+	0.217995i
$551$	−2.23982			−0.0954195
$552$	1.58490	+	4.87781i	0.0674577	+	0.207613i
$553$	38.0507	+	27.6454i	1.61808	+	1.17560i
$554$	−16.9294	+	12.2999i	−0.719260	+	0.522573i
$555$	5.06059	−	15.5749i	0.214810	−	0.661117i
$556$	3.20060	−	9.85044i	0.135736	−	0.417752i
$557$	23.7955	−	17.2884i	1.00825	−	0.732535i	0.0444072	−	0.999014i	$-0.485860\pi$
$557$	23.7955	−	17.2884i	1.00825	−	0.732535i	0.963841	+	0.266478i	$0.0858601\pi$
$558$	0.677471	+	0.492212i	0.0286797	+	0.0208370i
$559$	9.15033	+	28.1618i	0.387018	+	1.19112i
$560$	8.97068			0.379080
$561$	0.273012	−	5.51182i	0.0115266	−	0.232709i
$562$	−8.63480			−0.364237
$563$	1.09008	+	3.35492i	0.0459414	+	0.141393i	0.971396	−	0.237466i	$-0.0763167\pi$
$563$	1.09008	+	3.35492i	0.0459414	+	0.141393i	−0.925455	+	0.378859i	$0.876317\pi$
$564$	−7.98690	−	5.80282i	−0.336309	−	0.244343i
$565$	2.31684	−	1.68328i	0.0974702	−	0.0708163i
$566$	1.95060	−	6.00332i	0.0819897	−	0.252338i
$567$	−3.42040	+	10.5269i	−0.143643	+	0.442089i
$568$	0.706079	−	0.512996i	0.0296264	−	0.0215248i
$569$	−18.9630	−	13.7774i	−0.794971	−	0.577580i	0.114464	−	0.993427i	$-0.463485\pi$
$569$	−18.9630	−	13.7774i	−0.794971	−	0.577580i	−0.909434	+	0.415847i	$0.863485\pi$
$570$	0.501411	+	1.54318i	0.0210018	+	0.0646368i
$571$	23.7470			0.993782			0.496891	−	0.867813i	$-0.334475\pi$
$571$	23.7470			0.993782			0.496891	+	0.867813i	$0.334475\pi$
$572$	−17.3620	+	4.70556i	−0.725943	+	0.196749i
$573$	23.7363			0.991599
$574$	−14.4799	−	44.5645i	−0.604378	−	1.86008i
$575$	8.36879	+	6.08029i	0.349003	+	0.253565i
$576$	1.75270	−	1.27341i	0.0730291	−	0.0530587i
$577$	−3.80245	+	11.7027i	−0.158298	+	0.487191i	−0.998480	−	0.0551133i	$-0.982448\pi$
$577$	−3.80245	+	11.7027i	−0.158298	+	0.487191i	0.840182	+	0.542304i	$0.182448\pi$
$578$	−4.22689	+	13.0090i	−0.175816	+	0.541105i
$579$	−6.76417	+	4.91446i	−0.281109	+	0.204238i
$580$	3.22045	+	2.33980i	0.133722	+	0.0971547i
$581$	6.68677	+	20.5798i	0.277414	+	0.853793i
$582$	−2.65249			−0.109949
$583$	21.2546	+	8.08901i	0.880276	+	0.335013i
$584$	9.78216			0.404789
$585$	6.45319	+	19.8609i	0.266806	+	0.821146i
$586$	10.2558	+	7.45127i	0.423663	+	0.307809i
$587$	20.8292	−	15.1333i	0.859713	−	0.624618i	−0.0680936	−	0.997679i	$-0.521692\pi$
$587$	20.8292	−	15.1333i	0.859713	−	0.624618i	0.927807	+	0.373061i	$0.121692\pi$
$588$	5.21305	−	16.0441i	0.214983	−	0.661648i
$589$	−0.119445	+	0.367612i	−0.00492163	+	0.0151472i
$590$	5.32684	−	3.87018i	0.219303	−	0.159333i
$591$	14.4533	+	10.5010i	0.594530	+	0.431952i
$592$	−3.11882	−	9.59873i	−0.128183	−	0.394506i
$593$	13.4292			0.551469			0.275735	−	0.961234i	$-0.411079\pi$
$593$	13.4292			0.551469			0.275735	+	0.961234i	$0.411079\pi$
$594$	−9.81031	+	12.1860i	−0.402522	+	0.499999i
$595$	−16.3490			−0.670244
$596$	4.39838	+	13.5368i	0.180165	+	0.554490i
$597$	10.9625	+	7.96473i	0.448666	+	0.325975i
$598$	−24.6495	+	17.9089i	−1.00799	+	0.732349i
$599$	10.2287	−	31.4806i	0.417931	−	1.28626i	−0.491671	−	0.870781i	$-0.663614\pi$
$599$	10.2287	−	31.4806i	0.417931	−	1.28626i	0.909602	−	0.415480i	$-0.136386\pi$
$600$	−0.519516	+	1.59891i	−0.0212091	+	0.0652750i
$601$	28.0079	−	20.3490i	1.14247	−	0.830052i	0.155007	−	0.987913i	$-0.450460\pi$
$601$	28.0079	−	20.3490i	1.14247	−	0.830052i	0.987461	+	0.157862i	$0.0504600\pi$
$602$	22.2943	+	16.1978i	0.908650	+	0.660173i
$603$	7.74275	+	23.8297i	0.315309	+	0.970422i
$604$	−14.2150			−0.578398
$605$	19.4540	+	1.93193i	0.790916	+	0.0785440i
$606$	−0.484551			−0.0196835
$607$	−12.2441	−	37.6836i	−0.496974	−	1.52953i	−0.813857	−	0.581065i	$-0.802636\pi$
$607$	−12.2441	−	37.6836i	−0.496974	−	1.52953i	0.316883	−	0.948465i	$-0.397364\pi$
$608$	0.809017	+	0.587785i	0.0328100	+	0.0238378i
$609$	8.35054	−	6.06702i	0.338381	−	0.245848i
$610$	−1.58883	+	4.88992i	−0.0643299	+	0.197987i
$611$	18.1232	−	55.7774i	0.733185	−	2.25651i
$612$	−3.19428	+	2.32078i	−0.129121	+	0.0938120i
$613$	−17.5798	−	12.7725i	−0.710043	−	0.515876i	0.173145	−	0.984896i	$-0.444607\pi$
$613$	−17.5798	−	12.7725i	−0.710043	−	0.515876i	−0.883187	+	0.469020i	$0.844607\pi$
$614$	8.23293	+	25.3384i	0.332254	+	1.02257i
$615$	−15.0631			−0.607403
$616$	−10.4979	+	13.0402i	−0.422974	+	0.525404i
$617$	7.82581			0.315055			0.157528	−	0.987515i	$-0.449648\pi$
$617$	7.82581			0.315055			0.157528	+	0.987515i	$0.449648\pi$
$618$	−1.02664	−	3.15967i	−0.0412975	−	0.127101i
$619$	10.8942	+	7.91509i	0.437874	+	0.318134i	0.784790	−	0.619762i	$-0.212771\pi$
$619$	10.8942	+	7.91509i	0.437874	+	0.318134i	−0.346915	+	0.937896i	$0.612771\pi$
$620$	0.555761	−	0.403784i	0.0223199	−	0.0162163i
$621$	−8.18829	+	25.2010i	−0.328585	+	1.01128i
$622$	−7.75141	+	23.8564i	−0.310803	+	0.956554i
$623$	−22.8898	+	16.6304i	−0.917059	+	0.666282i
$624$	−4.00607	−	2.91058i	−0.160371	−	0.116516i
$625$	−3.83247	−	11.7951i	−0.153299	−	0.471805i
$626$	34.1330			1.36423
$627$	−2.83002	−	1.07704i	−0.113020	−	0.0430128i
$628$	13.8523			0.552767
$629$	5.68403	+	17.4936i	0.226637	+	0.697517i
$630$	15.7229	+	11.4233i	0.626415	+	0.455117i
$631$	−14.3803	+	10.4479i	−0.572469	+	0.415923i	−0.836001	−	0.548727i	$-0.815113\pi$
$631$	−14.3803	+	10.4479i	−0.572469	+	0.415923i	0.263532	+	0.964651i	$0.415113\pi$
$632$	2.87944	−	8.86201i	0.114538	−	0.352512i
$633$	−4.97271	+	15.3044i	−0.197648	+	0.608297i
$634$	24.4105	−	17.7352i	0.969463	−	0.704356i
$635$	22.5843	+	16.4085i	0.896231	+	0.651150i
$636$	1.93453	+	5.95388i	0.0767092	+	0.236087i
$637$	100.217			3.97074
$638$	−7.16997	+	1.94325i	−0.283862	+	0.0769339i
$639$	1.89080			0.0747988
$640$	−0.549198	−	1.69026i	−0.0217089	−	0.0668133i
$641$	−24.1415	−	17.5398i	−0.953532	−	0.692782i	−0.00189244	−	0.999998i	$-0.500602\pi$
$641$	−24.1415	−	17.5398i	−0.953532	−	0.692782i	−0.951640	+	0.307217i	$0.900602\pi$
$642$	−6.55029	+	4.75906i	−0.258519	+	0.187825i
$643$	−5.99992	+	18.4658i	−0.236614	+	0.728222i	0.760290	+	0.649584i	$0.225057\pi$
$643$	−5.99992	+	18.4658i	−0.236614	+	0.728222i	−0.996903	+	0.0786377i	$0.974943\pi$
$644$	−8.76224	+	26.9674i	−0.345280	+	1.06266i
$645$	7.16683	−	5.20700i	0.282194	−	0.205026i
$646$	−1.47443	−	1.07124i	−0.0580106	−	0.0421472i
$647$	−7.09297	−	21.8299i	−0.278853	−	0.858222i	−0.988174	−	0.153336i	$-0.950998\pi$
$647$	−7.09297	−	21.8299i	−0.278853	−	0.858222i	0.709321	−	0.704886i	$-0.249002\pi$
$648$	2.19288			0.0861446
$649$	−0.607877	+	12.2724i	−0.0238613	+	0.481734i
$650$	−9.98729			−0.391734
$651$	−0.550440	−	1.69408i	−0.0215734	−	0.0663962i
$652$	−8.84645	−	6.42732i	−0.346454	−	0.251713i
$653$	−28.4511	+	20.6709i	−1.11338	+	0.808915i	−0.983192	−	0.182574i	$-0.941557\pi$
$653$	−28.4511	+	20.6709i	−1.11338	+	0.808915i	−0.130185	+	0.991490i	$0.541557\pi$
$654$	−0.571851	+	1.75997i	−0.0223611	+	0.0688205i
$655$	−7.49589	+	23.0700i	−0.292889	+	0.901418i
$656$	−7.51036	+	5.45660i	−0.293230	+	0.213044i
$657$	17.1452	+	12.4567i	0.668897	+	0.485982i
$658$	−16.8662	−	51.9088i	−0.657513	−	2.02362i
$659$	14.4098			0.561325			0.280662	−	0.959807i	$-0.409446\pi$
$659$	14.4098			0.561325			0.280662	+	0.959807i	$0.409446\pi$
$660$	2.94394	+	4.50492i	0.114593	+	0.175354i
$661$	−19.8395			−0.771668			−0.385834	−	0.922568i	$-0.626086\pi$
$661$	−19.8395			−0.771668			−0.385834	+	0.922568i	$0.626086\pi$
$662$	3.32878	+	10.2449i	0.129377	+	0.398180i
$663$	7.30104	+	5.30452i	0.283549	+	0.206010i
$664$	3.46827	−	2.51985i	0.134595	−	0.0977890i
$665$	−2.77209	+	8.53162i	−0.107497	+	0.330842i
$666$	6.75677	−	20.7952i	0.261820	−	0.805798i
$667$	−10.1794	+	7.39580i	−0.394150	+	0.286367i
$668$	−3.15873	−	2.29495i	−0.122215	−	0.0887944i
$669$	2.86064	+	8.80413i	0.110599	+	0.340387i
$670$	20.5546			0.794095
$671$	−5.24888	−	8.03204i	−0.202631	−	0.310073i
$672$	−4.60833			−0.177770
$673$	5.36860	+	16.5228i	0.206944	+	0.636909i	0.999628	+	0.0272757i	$0.00868319\pi$
$673$	5.36860	+	16.5228i	0.206944	+	0.636909i	−0.792684	+	0.609633i	$0.791317\pi$
$674$	3.93485	+	2.85883i	0.151565	+	0.110118i
$675$	−7.02695	+	5.10538i	−0.270467	+	0.196506i
$676$	5.07300	−	15.6131i	0.195115	−	0.600504i
$677$	−3.93639	+	12.1150i	−0.151288	+	0.465616i	−0.997766	−	0.0668078i	$-0.978719\pi$
$677$	−3.93639	+	12.1150i	−0.151288	+	0.465616i	0.846478	+	0.532423i	$0.178719\pi$
$678$	−1.19019	+	0.864720i	−0.0457088	+	0.0332094i
$679$	−11.8638	−	8.61958i	−0.455292	−	0.330789i
$680$	1.00091	+	3.08048i	0.0383831	+	0.118131i
$681$	8.37169			0.320804
$682$	−0.0634211	+	1.28041i	−0.00242852	+	0.0490293i
$683$	3.11068			0.119027			0.0595134	−	0.998228i	$-0.481045\pi$
$683$	3.11068			0.119027			0.0595134	+	0.998228i	$0.481045\pi$
$684$	0.669471	+	2.06042i	0.0255979	+	0.0787821i
$685$	−12.9826	−	9.43241i	−0.496040	−	0.360394i
$686$	46.8691	−	34.0524i	1.78947	−	1.30013i
$687$	−0.129272	+	0.397859i	−0.00493205	+	0.0151793i
$688$	1.68710	−	5.19236i	0.0643200	−	0.197957i
$689$	−30.0873	+	21.8597i	−1.14623	+	0.832788i
$690$	7.37433	+	5.35776i	0.280736	+	0.203967i
$691$	10.7129	+	32.9708i	0.407536	+	1.25427i	0.918759	+	0.394819i	$0.129193\pi$
$691$	10.7129	+	32.9708i	0.407536	+	1.25427i	−0.511223	+	0.859448i	$0.670807\pi$
$692$	−8.63863			−0.328392
$693$	−35.0052	+	9.48732i	−1.32974	+	0.360393i
$694$	8.80331			0.334169
$695$	−5.68824	−	17.5066i	−0.215767	−	0.664063i
$696$	−1.65438	−	1.20198i	−0.0627091	−	0.0455609i
$697$	13.6876	−	9.94462i	0.518455	−	0.376679i
$698$	6.90097	−	21.2390i	0.261206	−	0.803908i
$699$	1.64713	−	5.06935i	0.0623002	−	0.191740i
$700$	−7.51949	+	5.46323i	−0.284210	+	0.206491i
$701$	1.08401	+	0.787582i	0.0409427	+	0.0297466i	0.608068	−	0.793885i	$-0.291945\pi$
$701$	1.08401	+	0.787582i	0.0409427	+	0.0297466i	−0.567126	+	0.823631i	$0.691945\pi$
$702$	−7.90562	−	24.3310i	−0.298378	−	0.918314i
$703$	10.0927			0.380654
$704$	3.09973	+	1.17969i	0.116826	+	0.0444611i
$705$	−17.5455			−0.660803
$706$	−2.46833	−	7.59674i	−0.0928969	−	0.285907i
$707$	−2.16726	−	1.57461i	−0.0815082	−	0.0592192i
$708$	−2.73645	+	1.98815i	−0.102842	+	0.0747193i
$709$	−4.40770	+	13.5655i	−0.165535	+	0.509463i	−0.999075	−	0.0429950i	$-0.986310\pi$
$709$	−4.40770	+	13.5655i	−0.165535	+	0.509463i	0.833541	+	0.552458i	$0.186310\pi$
$710$	0.479318	−	1.47519i	0.0179885	−	0.0553629i
$711$	16.3318	−	11.8657i	0.612489	−	0.444999i
$712$	4.53484	+	3.29476i	0.169950	+	0.123476i
$713$	0.670996	+	2.06511i	0.0251290	+	0.0773391i
$714$	8.39866			0.314312
$715$	−20.0478	+	24.9027i	−0.749747	+	0.931310i
$716$	−6.23923			−0.233171
$717$	2.17113	+	6.68206i	0.0810824	+	0.249546i
$718$	21.2479	+	15.4375i	0.792966	+	0.576123i
$719$	26.4342	−	19.2056i	0.985830	−	0.716247i	0.0268260	−	0.999640i	$-0.491460\pi$
$719$	26.4342	−	19.2056i	0.985830	−	0.716247i	0.959004	+	0.283393i	$0.0914600\pi$
$720$	1.18981	−	3.66186i	0.0443417	−	0.136470i
$721$	5.67586	−	17.4685i	0.211380	−	0.650561i
$722$	−0.809017	+	0.587785i	−0.0301085	+	0.0218751i
$723$	8.28700	+	6.02086i	0.308197	+	0.223918i
$724$	−8.08218	−	24.8744i	−0.300372	−	0.924449i
$725$	−4.12444			−0.153178
$726$	−9.99370	−	0.992451i	−0.370901	−	0.0368333i
$727$	−7.95801			−0.295146			−0.147573	−	0.989051i	$-0.547146\pi$
$727$	−7.95801			−0.295146			−0.147573	+	0.989051i	$0.547146\pi$
$728$	−8.45975	−	26.0364i	−0.313539	−	0.964974i
$729$	−6.60857	−	4.80141i	−0.244762	−	0.177830i
$730$	14.0650	−	10.2188i	0.520568	−	0.378214i
$731$	−3.07473	+	9.46304i	−0.113723	+	0.350003i
$732$	0.816200	−	2.51201i	0.0301676	−	0.0928464i
$733$	19.3146	−	14.0329i	0.713401	−	0.518316i	−0.170868	−	0.985294i	$-0.554657\pi$
$733$	19.3146	−	14.0329i	0.713401	−	0.518316i	0.884269	+	0.466978i	$0.154657\pi$
$734$	12.5456	+	9.11489i	0.463065	+	0.336437i
$735$	−9.26484	−	28.5143i	−0.341739	−	1.05176i
$736$	5.61764			0.207069
$737$	−24.0541	+	29.8791i	−0.886044	+	1.10061i
$738$	−20.1119			−0.740329
$739$	−2.55021	−	7.84875i	−0.0938111	−	0.288721i	0.893131	−	0.449797i	$-0.148504\pi$
$739$	−2.55021	−	7.84875i	−0.0938111	−	0.288721i	−0.986942	+	0.161076i	$0.948504\pi$
$740$	−14.5115	−	10.5432i	−0.533452	−	0.387576i
$741$	4.00607	−	2.91058i	0.147167	−	0.106923i
$742$	−10.6952	+	32.9166i	−0.392634	+	1.20840i
$743$	−1.30512	+	4.01675i	−0.0478802	+	0.147360i	−0.972138	−	0.234408i	$-0.924685\pi$
$743$	−1.30512	+	4.01675i	−0.0478802	+	0.147360i	0.924258	+	0.381768i	$0.124685\pi$
$744$	−0.285500	+	0.207428i	−0.0104669	+	0.00760468i
$745$	20.4651	+	14.8688i	0.749785	+	0.544750i
$746$	−5.39624	−	16.6079i	−0.197570	−	0.608059i
$747$	9.28763			0.339817
$748$	−5.64924	−	2.14997i	−0.206557	−	0.0786107i
$749$	−44.7628			−1.63560
$750$	3.43036	+	10.5576i	0.125259	+	0.385507i
$751$	−28.8155	−	20.9357i	−1.05149	−	0.763955i	−0.0789977	−	0.996875i	$-0.525172\pi$
$751$	−28.8155	−	20.9357i	−1.05149	−	0.763955i	−0.972496	+	0.232920i	$0.925172\pi$
$752$	−8.74809	+	6.35586i	−0.319010	+	0.231774i
$753$	−0.830984	+	2.55751i	−0.0302827	+	0.0932007i
$754$	3.75398	−	11.5535i	0.136712	−	0.420755i
$755$	−20.4385	+	14.8495i	−0.743834	+	0.540427i
$756$	−19.2617	−	13.9944i	−0.700540	−	0.508972i
$757$	11.8818	+	36.5683i	0.431850	+	1.32910i	0.896281	+	0.443487i	$0.146259\pi$
$757$	11.8818	+	36.5683i	0.431850	+	1.32910i	−0.464431	+	0.885609i	$0.653741\pi$
$758$	−31.6595			−1.14992
$759$	−16.4181	+	4.44973i	−0.595939	+	0.161515i
$760$	1.77724			0.0644673
$761$	0.775031	+	2.38530i	0.0280948	+	0.0864670i	0.964121	−	0.265464i	$-0.0855251\pi$
$761$	0.775031	+	2.38530i	0.0280948	+	0.0864670i	−0.936026	+	0.351931i	$0.885525\pi$
$762$	−11.6018	−	8.42920i	−0.420289	−	0.305358i
$763$	−8.27698	+	6.01358i	−0.299647	+	0.217706i
$764$	8.03399	−	24.7261i	0.290659	−	0.894558i
$765$	−2.16842	+	6.67372i	−0.0783996	+	0.241289i
$766$	4.93407	−	3.58481i	0.178275	−	0.129525i
$767$	−16.2562	−	11.8108i	−0.586978	−	0.426465i
$768$	0.282129	+	0.868303i	0.0101804	+	0.0313322i
$769$	1.24222			0.0447955			0.0223978	−	0.999749i	$-0.492870\pi$
$769$	1.24222			0.0447955			0.0223978	+	0.999749i	$0.492870\pi$
$770$	−1.47189	+	29.7159i	−0.0530432	+	1.07089i
$771$	19.3445			0.696674
$772$	2.82992	+	8.70961i	0.101851	+	0.313466i
$773$	−21.7100	−	15.7732i	−0.780854	−	0.567324i	0.124381	−	0.992235i	$-0.460306\pi$
$773$	−21.7100	−	15.7732i	−0.780854	−	0.567324i	−0.905235	+	0.424911i	$0.860306\pi$
$774$	9.56897	−	6.95227i	0.343950	−	0.249894i
$775$	−0.219947	+	0.676927i	−0.00790073	+	0.0243159i
$776$	−0.897782	+	2.76309i	−0.0322285	+	0.0991891i
$777$	−37.6278	+	27.3382i	−1.34989	+	0.980753i
$778$	25.9067	+	18.8223i	0.928800	+	0.674813i
$779$	−2.86870	−	8.82896i	−0.102782	−	0.316330i
$780$	−8.80050			−0.315108
$781$	1.58348	+	2.42310i	0.0566614	+	0.0867054i
$782$	−10.2381			−0.366114
$783$	−3.26477	−	10.0479i	−0.116673	−	0.359084i
$784$	−14.9487	−	10.8608i	−0.533881	−	0.387887i
$785$	19.9171	−	14.4706i	0.710871	−	0.516478i
$786$	3.85072	−	11.8513i	0.137351	−	0.422721i
$787$	1.48275	−	4.56343i	0.0528543	−	0.162669i	−0.921145	−	0.389219i	$-0.872745\pi$
$787$	1.48275	−	4.56343i	0.0528543	−	0.162669i	0.973999	+	0.226551i	$0.0727448\pi$
$788$	15.8308	−	11.5018i	0.563949	−	0.409733i
$789$	−2.79612	−	2.03150i	−0.0995446	−	0.0723234i
$790$	−5.11746	−	15.7499i	−0.182071	−	0.560357i
$791$	−8.13338			−0.289190
$792$	3.93067	+	6.01486i	0.139670	+	0.213729i
$793$	15.6908			0.557197
$794$	3.09330	+	9.52021i	0.109777	+	0.337860i
$795$	9.00115	+	6.53972i	0.319238	+	0.231940i
$796$	12.0073	−	8.72381i	0.425587	−	0.309207i
$797$	−1.28369	+	3.95078i	−0.0454705	+	0.139944i	−0.971214	−	0.238208i	$-0.923440\pi$
$797$	−1.28369	+	3.95078i	−0.0454705	+	0.139944i	0.925744	+	0.378151i	$0.123440\pi$
$798$	1.42405	−	4.38278i	0.0504109	−	0.155149i
$799$	15.9433	−	11.5835i	0.564035	−	0.409795i
$800$	1.48974	+	1.08236i	0.0526701	+	0.0382671i
$801$	3.75264	+	11.5494i	0.132593	+	0.408079i
$802$	−5.31105			−0.187540
$803$	−1.60504	+	32.4040i	−0.0566405	+	1.14351i
$804$	−10.5591			−0.372392
$805$	15.5726	+	47.9275i	0.548862	+	1.68922i
$806$	−1.69605	−	1.23225i	−0.0597407	−	0.0434041i
$807$	21.4497	−	15.5841i	0.755066	−	0.548587i
$808$	−0.164005	+	0.504755i	−0.00576967	+	0.0177572i
$809$	−5.54642	+	17.0701i	−0.195002	+	0.600154i	0.804975	+	0.593309i	$0.202179\pi$
$809$	−5.54642	+	17.0701i	−0.195002	+	0.600154i	−0.999977	+	0.00684496i	$0.997821\pi$
$810$	3.15297	−	2.29077i	0.110784	−	0.0804893i
$811$	6.72613	+	4.88682i	0.236186	+	0.171600i	0.699583	−	0.714552i	$-0.253369\pi$
$811$	6.72613	+	4.88682i	0.236186	+	0.171600i	−0.463396	+	0.886151i	$0.653369\pi$
$812$	−3.49361	−	10.7522i	−0.122602	−	0.377329i
$813$	15.1136			0.530058
$814$	32.3081	−	8.75634i	1.13240	−	0.306910i
$815$	−19.4338			−0.680736
$816$	−0.514178	−	1.58248i	−0.0179998	−	0.0553978i
$817$	4.41688	+	3.20905i	0.154527	+	0.112271i
$818$	−15.0008	+	10.8987i	−0.524490	+	0.381065i
$819$	18.3277	−	56.4067i	0.640420	−	1.97101i
$820$	−5.09838	+	15.6912i	−0.178043	+	0.547960i
$821$	−40.5255	+	29.4435i	−1.41435	+	1.02759i	−0.421678	+	0.906746i	$0.638559\pi$
$821$	−40.5255	+	29.4435i	−1.41435	+	1.02759i	−0.992672	+	0.120840i	$0.961441\pi$
$822$	6.66930	+	4.84553i	0.232618	+	0.169007i
$823$	8.31520	+	25.5916i	0.289850	+	0.892066i	0.984903	+	0.173108i	$0.0553808\pi$
$823$	8.31520	+	25.5916i	0.289850	+	0.892066i	−0.695053	+	0.718958i	$0.744619\pi$
$824$	−3.63890			−0.126767
$825$	−5.21123	−	1.98327i	−0.181432	−	0.0690487i
$826$	−18.7001			−0.650661
$827$	2.12545	+	6.54147i	0.0739093	+	0.227469i	0.981186	−	0.193065i	$-0.0618427\pi$
$827$	2.12545	+	6.54147i	0.0739093	+	0.227469i	−0.907277	+	0.420534i	$0.861843\pi$
$828$	9.84602	+	7.15355i	0.342173	+	0.248603i
$829$	−21.1006	+	15.3305i	−0.732853	+	0.532449i	−0.890465	−	0.455052i	$-0.849621\pi$
$829$	−21.1006	+	15.3305i	−0.732853	+	0.532449i	0.157612	+	0.987501i	$0.449621\pi$
$830$	2.35442	−	7.24616i	0.0817231	−	0.251518i
$831$	5.90378	−	18.1700i	0.204800	−	0.630309i
$832$	−4.38787	+	3.18797i	−0.152122	+	0.110523i
$833$	27.2439	+	19.7938i	0.943943	+	0.685815i
$834$	2.92211	+	8.99333i	0.101184	+	0.311414i
$835$	−6.93907			−0.240136
$836$	−2.07982	+	2.58348i	−0.0719320	+	0.0893514i
$837$	−1.82323			−0.0630200
$838$	3.56724	+	10.9788i	0.123228	+	0.379258i
$839$	−24.1324	−	17.5332i	−0.833142	−	0.605313i	0.0873047	−	0.996182i	$-0.472175\pi$
$839$	−24.1324	−	17.5332i	−0.833142	−	0.605313i	−0.920446	+	0.390869i	$0.872175\pi$
$840$	−6.62594	+	4.81403i	−0.228617	+	0.166100i
$841$	−7.41122	+	22.8094i	−0.255559	+	0.786531i
$842$	10.4225	−	32.0772i	0.359183	−	1.10545i
$843$	6.37786	−	4.63378i	0.219665	−	0.159596i
$844$	14.2595	+	10.3601i	0.490832	+	0.356610i
$845$	−9.01595	−	27.7482i	−0.310158	−	0.954568i
$846$	−23.4264			−0.805416
$847$	−41.4740	−	36.9147i	−1.42506	−	1.26840i
$848$	6.85692			0.235468
$849$	1.78087	+	5.48095i	0.0611193	+	0.188106i
$850$	−2.71504	−	1.97259i	−0.0931249	−	0.0676592i
$851$	45.8690	−	33.3257i	1.57237	−	1.14239i
$852$	−0.246231	+	0.757821i	−0.00843573	+	0.0259625i
$853$	−11.0489	+	34.0050i	−0.378307	+	1.16431i	0.562914	+	0.826516i	$0.309680\pi$
$853$	−11.0489	+	34.0050i	−0.378307	+	1.16431i	−0.941221	+	0.337793i	$0.890320\pi$
$854$	11.8137	−	8.58316i	0.404257	−	0.293710i
$855$	3.11497	+	2.26316i	0.106530	+	0.0773983i
$856$	2.74044	+	8.43421i	0.0936663	+	0.288275i
$857$	−53.7988			−1.83773			−0.918867	−	0.394568i	$-0.870894\pi$
$857$	−53.7988			−1.83773			−0.918867	+	0.394568i	$0.870894\pi$
$858$	10.2988	−	12.7928i	0.351595	−	0.436739i
$859$	40.7851			1.39157			0.695785	−	0.718250i	$-0.255057\pi$
$859$	40.7851			1.39157			0.695785	+	0.718250i	$0.255057\pi$
$860$	−2.99838	−	9.22807i	−0.102244	−	0.314675i
$861$	34.6103	+	25.1458i	1.17951	+	0.856967i
$862$	8.11546	−	5.89623i	0.276414	−	0.200826i
$863$	−10.7945	+	33.2221i	−0.367449	+	1.13089i	0.580984	+	0.813915i	$0.302668\pi$
$863$	−10.7945	+	33.2221i	−0.367449	+	1.13089i	−0.948433	+	0.316978i	$0.897332\pi$
$864$	−1.45760	+	4.48605i	−0.0495887	+	0.152618i
$865$	−12.4208	+	9.02423i	−0.422319	+	0.306833i
$866$	6.39715	+	4.64780i	0.217384	+	0.157939i
$867$	−3.85910	−	11.8771i	−0.131062	−	0.403367i
$868$	−1.95102			−0.0662221
$869$	28.8835	+	10.9924i	0.979806	+	0.372891i
$870$	−3.63433			−0.123215
$871$	−19.3839	−	59.6576i	−0.656800	−	2.02142i
$872$	1.63981	+	1.19139i	0.0555309	+	0.0403456i
$873$	−5.09208	+	3.69961i	−0.172341	+	0.125213i
$874$	−1.73595	+	5.34269i	−0.0587192	+	0.180719i
$875$	−18.9650	+	58.3684i	−0.641135	+	1.97321i
$876$	−7.22532	+	5.24950i	−0.244121	+	0.177364i
$877$	1.90761	+	1.38596i	0.0644154	+	0.0468005i	0.619527	−	0.784975i	$-0.287324\pi$
$877$	1.90761	+	1.38596i	0.0644154	+	0.0468005i	−0.555112	+	0.831776i	$0.687324\pi$
$878$	7.95424	+	24.4806i	0.268443	+	0.826182i
$879$	−11.5738			−0.390375
$880$	5.68919	−	1.54192i	0.191783	−	0.0519781i
$881$	24.8750			0.838060			0.419030	−	0.907972i	$-0.362370\pi$
$881$	24.8750			0.838060			0.419030	+	0.907972i	$0.362370\pi$
$882$	−12.3702	−	38.0715i	−0.416526	−	1.28194i
$883$	−29.0306	−	21.0920i	−0.976958	−	0.709802i	−0.0199315	−	0.999801i	$-0.506345\pi$
$883$	−29.0306	−	21.0920i	−0.976958	−	0.709802i	−0.957027	+	0.290000i	$0.906345\pi$
$884$	7.99687	−	5.81006i	0.268964	−	0.195414i
$885$	−1.85763	+	5.71720i	−0.0624436	+	0.192182i
$886$	−7.47891	+	23.0177i	−0.251259	+	0.773295i
$887$	40.3753	−	29.3344i	1.35567	−	0.984952i	0.356963	−	0.934119i	$-0.383812\pi$
$887$	40.3753	−	29.3344i	1.35567	−	0.984952i	0.998707	−	0.0508331i	$-0.0161877\pi$
$888$	7.45470	+	5.41615i	0.250163	+	0.181754i
$889$	−24.4999	−	75.4029i	−0.821700	−	2.52893i
$890$	9.96210			0.333930
$891$	−0.359804	+	7.26407i	−0.0120539	+	0.243356i
$892$	10.1395			0.339495
$893$	−3.34147	−	10.2840i	−0.111818	−	0.344141i
$894$	−10.5132	−	7.63826i	−0.351613	−	0.255461i
$895$	−8.97088	+	6.51773i	−0.299863	+	0.217864i
$896$	−1.55977	+	4.80049i	−0.0521083	+	0.160373i
$897$	8.59601	−	26.4558i	0.287012	−	0.883333i
$898$	−29.5346	+	21.4581i	−0.985582	+	0.716067i
$899$	−0.700414	−	0.508880i	−0.0233601	−	0.0169721i
$900$	1.23277	+	3.79409i	0.0410925	+	0.126470i
$901$	−12.4967			−0.416325
$902$	−16.8430	−	25.7739i	−0.560812	−	0.858176i
$903$	−25.1595			−0.837256
$904$	0.497937	+	1.53249i	0.0165611	+	0.0509700i
$905$	−37.6054	−	27.3219i	−1.25005	−	0.908211i
$906$	10.4995	−	7.62832i	0.348822	−	0.253434i
$907$	−1.34859	+	4.15053i	−0.0447792	+	0.137816i	−0.970946	−	0.239297i	$-0.923083\pi$
$907$	−1.34859	+	4.15053i	−0.0447792	+	0.137816i	0.926167	+	0.377113i	$0.123083\pi$
$908$	2.83355	−	8.72077i	0.0940346	−	0.289409i
$909$	−0.930211	+	0.675838i	−0.0308532	+	0.0224161i
$910$	−39.3622	−	28.5983i	−1.30484	−	0.948024i
$911$	13.9895	+	43.0553i	0.463493	+	1.42648i	0.860868	+	0.508828i	$0.169921\pi$
$911$	13.9895	+	43.0553i	0.463493	+	1.42648i	−0.397375	+	0.917656i	$0.630079\pi$
$912$	−0.912987			−0.0302320
$913$	7.77808	+	11.9023i	0.257417	+	0.393909i
$914$	15.7612			0.521334
$915$	−1.45058	−	4.46444i	−0.0479548	−	0.147590i
$916$	0.370695	+	0.269325i	0.0122481	+	0.00889876i
$917$	55.7354	−	40.4941i	1.84054	−	1.33723i
$918$	2.65648	−	8.17579i	0.0876768	−	0.269841i
$919$	−15.6540	+	48.1781i	−0.516378	+	1.58925i	0.264383	+	0.964418i	$0.414832\pi$
$919$	−15.6540	+	48.1781i	−0.516378	+	1.58925i	−0.780761	+	0.624830i	$0.785168\pi$
$920$	8.07714	−	5.86839i	0.266295	−	0.193475i
$921$	−19.6786	−	14.2974i	−0.648433	−	0.471114i
$922$	2.04304	+	6.28782i	0.0672838	+	0.207078i
$923$	−4.73360			−0.155808
$924$	0.756125	−	15.2654i	0.0248747	−	0.502195i
$925$	18.5849			0.611066
$926$	−10.0352	−	30.8853i	−0.329778	−	1.01495i
$927$	−6.37790	−	4.63382i	−0.209478	−	0.152195i
$928$	−1.81205	+	1.31653i	−0.0594835	+	0.0432173i
$929$	−0.437929	+	1.34781i	−0.0143680	+	0.0442201i	−0.957983	−	0.286823i	$-0.907401\pi$
$929$	−0.437929	+	1.34781i	−0.0143680	+	0.0442201i	0.943615	+	0.331044i	$0.107401\pi$
$930$	−0.193811	+	0.596487i	−0.00635530	+	0.0195596i
$931$	14.9487	−	10.8608i	0.489923	−	0.355950i
$932$	−4.72322	−	3.43162i	−0.154714	−	0.112407i
$933$	−7.07694	−	21.7806i	−0.231689	−	0.713065i
$934$	38.0595			1.24534
$935$	−10.3685	+	2.81014i	−0.339087	+	0.0919013i
$936$	−11.7502			−0.384068
$937$	0.121226	+	0.373094i	0.00396027	+	0.0121884i	0.953017	−	0.302916i	$-0.0979603\pi$
$937$	0.121226	+	0.373094i	0.00396027	+	0.0121884i	−0.949057	+	0.315105i	$0.897960\pi$
$938$	−47.2281	−	34.3132i	−1.54205	−	1.12037i
$939$	−25.2114	+	18.3171i	−0.822742	+	0.597757i
$940$	−5.93860	+	18.2771i	−0.193696	+	0.596135i
$941$	7.65106	−	23.5476i	0.249418	−	0.767628i	−0.745461	−	0.666549i	$-0.767771\pi$
$941$	7.65106	−	23.5476i	0.249418	−	0.767628i	0.994878	−	0.101079i	$-0.0322295\pi$
$942$	−10.2316	+	7.43370i	−0.333364	+	0.242203i
$943$	−42.1905	−	30.6532i	−1.37391	−	0.998205i
$944$	1.14485	+	3.52348i	0.0372617	+	0.114680i
$945$	−42.3139			−1.37647
$946$	16.9232	+	6.44057i	0.550221	+	0.209401i
$947$	30.8771			1.00337			0.501685	−	0.865050i	$-0.332714\pi$
$947$	30.8771			1.00337			0.501685	+	0.865050i	$0.332714\pi$
$948$	2.62889	+	8.09091i	0.0853825	+	0.262780i
$949$	−42.9228	−	31.1853i	−1.39333	−	1.01232i
$950$	−1.48974	+	1.08236i	−0.0483334	+	0.0351163i
$951$	−8.51266	+	26.1993i	−0.276042	+	0.849570i
$952$	2.84268	−	8.74886i	0.0921317	−	0.283552i
$953$	−6.30022	+	4.57738i	−0.204084	+	0.148276i	−0.685133	−	0.728418i	$-0.740256\pi$
$953$	−6.30022	+	4.57738i	−0.204084	+	0.148276i	0.481049	+	0.876694i	$0.340256\pi$
$954$	12.0181	+	8.73167i	0.389101	+	0.282698i
$955$	−14.2783	−	43.9442i	−0.462036	−	1.42200i
$956$	7.69554			0.248892
$957$	4.25308	−	5.28302i	0.137482	−	0.170776i
$958$	30.0892			0.972138
$959$	14.0838	+	43.3454i	0.454789	+	1.39970i
$960$	1.31271	+	0.953740i	0.0423675	+	0.0307818i
$961$	24.9587	−	18.1335i	0.805118	−	0.584952i
$962$	−16.9155	+	52.0607i	−0.545379	+	1.67850i
$963$	−5.93704	+	18.2723i	−0.191318	+	0.588817i
$964$	9.07680	−	6.59468i	0.292344	−	0.212400i
$965$	13.1673	+	9.56659i	0.423870	+	0.307960i
$966$	−7.99981	−	24.6209i	−0.257390	−	0.792164i
$967$	13.5476			0.435662			0.217831	−	0.975987i	$-0.430102\pi$
$967$	13.5476			0.435662			0.217831	+	0.975987i	$0.430102\pi$
$968$	−4.41638	+	10.0745i	−0.141948	+	0.323807i
$969$	1.66391			0.0534526
$970$	1.59557	+	4.91067i	0.0512308	+	0.157672i
$971$	−36.8638	−	26.7831i	−1.18301	−	0.859510i	−0.190506	−	0.981686i	$-0.561013\pi$
$971$	−36.8638	−	26.7831i	−1.18301	−	0.859510i	−0.992508	+	0.122176i	$0.961013\pi$
$972$	−13.0679	+	9.49438i	−0.419153	+	0.304532i
$973$	−16.1551	+	49.7204i	−0.517910	+	1.59396i
$974$	−0.832472	+	2.56209i	−0.0266741	+	0.0820945i
$975$	7.37684	−	5.35959i	0.236248	−	0.171644i
$976$	−2.34049	−	1.70047i	−0.0749173	−	0.0544306i
$977$	−6.64339	−	20.4462i	−0.212541	−	0.654133i	−0.999319	−	0.0368976i	$-0.988252\pi$
$977$	−6.64339	−	20.4462i	−0.212541	−	0.654133i	0.786778	−	0.617236i	$-0.211748\pi$
$978$	9.98334			0.319232
$979$	−11.6582	+	14.4814i	−0.372596	+	0.462826i
$980$	−32.8391			−1.04901
$981$	1.35696	+	4.17629i	0.0433244	+	0.133339i
$982$	−22.5578	−	16.3892i	−0.719849	−	0.523001i
$983$	−11.0303	+	8.01395i	−0.351810	+	0.255605i	−0.749628	−	0.661859i	$-0.769768\pi$
$983$	−11.0303	+	8.01395i	−0.351810	+	0.255605i	0.397818	+	0.917464i	$0.369768\pi$
$984$	2.61909	−	8.06073i	0.0834936	−	0.256967i
$985$	10.7467	−	33.0749i	0.342418	−	1.05385i
$986$	3.30245	−	2.39937i	0.105172	−	0.0764116i
$987$	40.3141	+	29.2899i	1.28321	+	0.932308i
$988$	−1.67602	−	5.15825i	−0.0533212	−	0.164106i
$989$	30.6699			0.975245
$990$	11.9349	+	4.54216i	0.379317	+	0.144359i
$991$	16.9742			0.539202			0.269601	−	0.962972i	$-0.413108\pi$
$991$	16.9742			0.539202			0.269601	+	0.962972i	$0.413108\pi$
$992$	0.119445	+	0.367612i	0.00379237	+	0.0116717i
$993$	−7.95655	−	5.78077i	−0.252493	−	0.183447i
$994$	−3.56395	+	2.58936i	−0.113042	+	0.0821296i
$995$	8.15110	−	25.0865i	0.258407	−	0.795296i
$996$	−1.20949	+	3.72243i	−0.0383242	+	0.117950i
$997$	33.0117	−	23.9844i	1.04549	−	0.759595i	0.0741421	−	0.997248i	$-0.476378\pi$
$997$	33.0117	−	23.9844i	1.04549	−	0.759595i	0.971350	+	0.237653i	$0.0763782\pi$
$998$	−16.9919	−	12.3453i	−0.537869	−	0.390785i
$999$	14.7112	+	45.2763i	0.465441	+	1.43248i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.f.f.115.2	✓	16
11.3	even	5		4598.2.a.ca.1.5		8
11.8	odd	10		4598.2.a.bx.1.5		8
11.9	even	5	inner	418.2.f.f.229.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.f.115.2	✓	16	1.1	even	1	trivial
418.2.f.f.229.2	yes	16	11.9	even	5	inner
4598.2.a.bx.1.5		8	11.8	odd	10
4598.2.a.ca.1.5		8	11.3	even	5

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{2} +(-0.738622 - 0.536641i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.549198 + 1.69026i) q^{5} +(0.282129 - 0.868303i) q^{6} +(4.08354 - 2.96686i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.669471 - 2.06042i) q^{9} +O(q^{10})\)	\(q+(0.309017 + 0.951057i) q^{2} +(-0.738622 - 0.536641i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.549198 + 1.69026i) q^{5} +(0.282129 - 0.868303i) q^{6} +(4.08354 - 2.96686i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.669471 - 2.06042i) q^{9} -1.77724 q^{10} +(2.07982 - 2.58348i) q^{11} +0.912987 q^{12} +(1.67602 + 5.15825i) q^{13} +(4.08354 + 2.96686i) q^{14} +(1.31271 - 0.953740i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-0.563182 + 1.73330i) q^{17} +(1.75270 - 1.27341i) q^{18} +(0.809017 + 0.587785i) q^{19} +(-0.549198 - 1.69026i) q^{20} -4.60833 q^{21} +(3.09973 + 1.17969i) q^{22} +5.61764 q^{23} +(0.282129 + 0.868303i) q^{24} +(1.48974 + 1.08236i) q^{25} +(-4.38787 + 3.18797i) q^{26} +(-1.45760 + 4.48605i) q^{27} +(-1.55977 + 4.80049i) q^{28} +(-1.81205 + 1.31653i) q^{29} +(1.31271 + 0.953740i) q^{30} +(0.119445 + 0.367612i) q^{31} +1.00000 q^{32} +(-2.92260 + 0.792100i) q^{33} -1.82249 q^{34} +(2.77209 + 8.53162i) q^{35} +(1.75270 + 1.27341i) q^{36} +(8.16517 - 5.93234i) q^{37} +(-0.309017 + 0.951057i) q^{38} +(1.53018 - 4.70942i) q^{39} +(1.43782 - 1.04464i) q^{40} +(-7.51036 - 5.45660i) q^{41} +(-1.42405 - 4.38278i) q^{42} +5.45957 q^{43} +(-0.164078 + 3.31256i) q^{44} +3.85031 q^{45} +(1.73595 + 5.34269i) q^{46} +(-8.74809 - 6.35586i) q^{47} +(-0.738622 + 0.536641i) q^{48} +(5.70988 - 17.5732i) q^{49} +(-0.569028 + 1.75129i) q^{50} +(1.34613 - 0.978024i) q^{51} +(-4.38787 - 3.18797i) q^{52} +(2.11890 + 6.52132i) q^{53} -4.71691 q^{54} +(3.22451 + 4.93427i) q^{55} -5.04753 q^{56} +(-0.282129 - 0.868303i) q^{57} +(-1.81205 - 1.31653i) q^{58} +(-2.99725 + 2.17763i) q^{59} +(-0.501411 + 1.54318i) q^{60} +(0.893988 - 2.75141i) q^{61} +(-0.312710 + 0.227197i) q^{62} +(-8.84680 - 6.42757i) q^{63} +(0.309017 + 0.951057i) q^{64} -9.63923 q^{65} +(-1.65646 - 2.53478i) q^{66} -11.5655 q^{67} +(-0.563182 - 1.73330i) q^{68} +(-4.14931 - 3.01465i) q^{69} +(-7.25743 + 5.27283i) q^{70} +(-0.269698 + 0.830045i) q^{71} +(-0.669471 + 2.06042i) q^{72} +(-7.91393 + 5.74981i) q^{73} +(8.16517 + 5.93234i) q^{74} +(-0.519516 - 1.59891i) q^{75} -1.00000 q^{76} +(0.828188 - 16.7203i) q^{77} +4.95177 q^{78} +(2.87944 + 8.86201i) q^{79} +(1.43782 + 1.04464i) q^{80} +(-1.77408 + 1.28895i) q^{81} +(2.86870 - 8.82896i) q^{82} +(-1.32476 + 4.07720i) q^{83} +(3.72822 - 2.70871i) q^{84} +(-2.62042 - 1.90384i) q^{85} +(1.68710 + 5.19236i) q^{86} +2.04493 q^{87} +(-3.20114 + 0.867591i) q^{88} -5.60537 q^{89} +(1.18981 + 3.66186i) q^{90} +(22.1479 + 16.0914i) q^{91} +(-4.54476 + 3.30196i) q^{92} +(0.109051 - 0.335626i) q^{93} +(3.34147 - 10.2840i) q^{94} +(-1.43782 + 1.04464i) q^{95} +(-0.738622 - 0.536641i) q^{96} +(-0.897782 - 2.76309i) q^{97} +18.4776 q^{98} +(-6.71543 - 2.55574i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 4 q^{4} + 4 q^{5} + 6 q^{7} - 4 q^{8} - 20 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 - 4 * q^4 + 4 * q^5 + 6 * q^7 - 4 * q^8 - 20 * q^9	\( 16 q - 4 q^{2} - 4 q^{4} + 4 q^{5} + 6 q^{7} - 4 q^{8} - 20 q^{9} + 4 q^{10} + 2 q^{11} - 14 q^{13} + 6 q^{14} - 10 q^{15} - 4 q^{16} + 8 q^{17} + 4 q^{19} + 4 q^{20} + 28 q^{21} + 2 q^{22} + 24 q^{23} - 4 q^{26} - 18 q^{27} - 14 q^{28} - 22 q^{29} - 10 q^{30} - 24 q^{31} + 16 q^{32} + 2 q^{33} + 8 q^{34} - 20 q^{35} + 6 q^{37} + 4 q^{38} + 72 q^{39} - 6 q^{40} - 14 q^{41} - 22 q^{42} + 56 q^{43} + 12 q^{44} - 56 q^{45} + 4 q^{46} - 38 q^{47} - 36 q^{49} + 56 q^{51} - 4 q^{52} + 22 q^{53} - 48 q^{54} - 6 q^{55} + 16 q^{56} - 22 q^{58} - 28 q^{59} + 12 q^{61} + 26 q^{62} - 20 q^{63} - 4 q^{64} - 32 q^{65} + 12 q^{66} - 44 q^{67} + 8 q^{68} + 64 q^{69} - 20 q^{70} + 16 q^{71} - 20 q^{72} + 12 q^{73} + 6 q^{74} + 32 q^{75} - 16 q^{76} - 12 q^{77} - 8 q^{78} + 48 q^{79} - 6 q^{80} - 64 q^{81} + 6 q^{82} + 14 q^{83} + 8 q^{84} + 6 q^{85} - 14 q^{86} + 84 q^{87} - 8 q^{88} - 56 q^{89} + 34 q^{90} + 26 q^{91} - 16 q^{92} - 46 q^{93} + 32 q^{94} + 6 q^{95} - 24 q^{97} + 64 q^{98} - 56 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 4 * q^4 + 4 * q^5 + 6 * q^7 - 4 * q^8 - 20 * q^9 + 4 * q^10 + 2 * q^11 - 14 * q^13 + 6 * q^14 - 10 * q^15 - 4 * q^16 + 8 * q^17 + 4 * q^19 + 4 * q^20 + 28 * q^21 + 2 * q^22 + 24 * q^23 - 4 * q^26 - 18 * q^27 - 14 * q^28 - 22 * q^29 - 10 * q^30 - 24 * q^31 + 16 * q^32 + 2 * q^33 + 8 * q^34 - 20 * q^35 + 6 * q^37 + 4 * q^38 + 72 * q^39 - 6 * q^40 - 14 * q^41 - 22 * q^42 + 56 * q^43 + 12 * q^44 - 56 * q^45 + 4 * q^46 - 38 * q^47 - 36 * q^49 + 56 * q^51 - 4 * q^52 + 22 * q^53 - 48 * q^54 - 6 * q^55 + 16 * q^56 - 22 * q^58 - 28 * q^59 + 12 * q^61 + 26 * q^62 - 20 * q^63 - 4 * q^64 - 32 * q^65 + 12 * q^66 - 44 * q^67 + 8 * q^68 + 64 * q^69 - 20 * q^70 + 16 * q^71 - 20 * q^72 + 12 * q^73 + 6 * q^74 + 32 * q^75 - 16 * q^76 - 12 * q^77 - 8 * q^78 + 48 * q^79 - 6 * q^80 - 64 * q^81 + 6 * q^82 + 14 * q^83 + 8 * q^84 + 6 * q^85 - 14 * q^86 + 84 * q^87 - 8 * q^88 - 56 * q^89 + 34 * q^90 + 26 * q^91 - 16 * q^92 - 46 * q^93 + 32 * q^94 + 6 * q^95 - 24 * q^97 + 64 * q^98 - 56 * q^99

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